I feel bad I can't understand the most simple of algebra

[BadFish]

Total pay = Hourly rate * number of hours per week + 1.5h

$550 = (10 * 40 = $400) + ( 1.5 * 15)

Darn, that's not right either! I'm not sure how to modify the second rate..

 

[Bohrok]

How many hours are overtime?

 

[BadFish]

10 hours overtime (50), 40 hours normal.

 

[Bohrok]

Actually you already have it here

To continue, again if someone gets $10/hour and works 50 hours,

How many hours does he/she get the normal pay rate?
How many hours does he/she get the overtime pay rate?
What's the amount he/she gets at the normal rate?
What's the amount of overtime pay?
10 hours over over time...
First we need to find out the normal rate.
$10/per hour (h)

1.5 x * 10 = $15, which is our new rate
$15 * 10 hours = $150
What's the total?
$400 + overtime pay (150) = $550

If you let h be the time spent working, you multiply it by the normal rate. The time that is beyond 40 hours needs to be multiplied by the 1.5 times the normal rate and added to the 40-hour normal pay.

 

[BadFish]

Actually you already have it here



If you let h be the time spent working, you multiply it by the normal rate. The time that is beyond 40 hours needs to be multiplied by the 1.5 times the normal rate and added to the 40-hour normal pay.

So...

10h + 1.5 * h

?

 

[symbolipoint]

You either did not read, did not see, or did not understand my post #28. Return to that posting and study it.

 

[BadFish]

40*p + 10*1.5*p

I did not include the units in that expression but you can supply them and analyze the result.

What do you mean by this?

replace p with 10, then,
40*p + 10*1.5*p
40*(10) + 10*1.5(10)
$400 + 10*(15)
$400 + $150 = 550
550 = 550

(Check...answering is right)

 

[Ouabache]

Good Job!
So this was a simulation, in order to have a better feel for the meaning of terms in the question you were trying to answer, which was:

Calculate your pay if you work more than 40 hours and are paid time and one half for every hour past 40.

The question is indirectly asking you, to develop an equation.
Remember in the first part you developed the simple equation by asking yourself, what are you given. You found ( https://www.physicsforums.com/showthread.php?t=317172,#8" )
Pay = p
Rate (amount of compensation/time) = r
Time (hours) = t

and developed the expression P = rt

This question does not tell you how much you earn up to and including 40hrs, but it is a good assumption, that you are earning the "normal rate" = r. So using this variable, what would be the "overtime rate"?

If the normal rate covers up to and including 40 hours, what would be a way to express any "time" worked over 40hrs?
(Hint: t will be in this expression).

 

[BadFish]

1.5 * r = overtime rate

example:
let normal rate = 10/hour then,

1.5 * 10 = New rate $15

Not sure on the second question..

I want to understand this so bad...going to keep trying to find the answer!

Time over 40 hours...

(1.5 * r)/t

example

one week, 7 days

(1.5 * r)/t
(1.5 * 10)/t
($15)/7

Hmm, that's not right!

perhaps

(1.5 * r * 10)/t

one week, 7 days
(1.5*[10]*10)/7 dys
($15 * 10)/7
($150/7)

$21.42 total for overtime rate in one week

 

[Mark44]

If you work 50 hours, how many overtime hours have you worked?
If you work h hours, how many overtime hours have you worked? You should have two answers for this, depending on the value of h.

 

[BadFish]

So one value for 40 hours, and one value for the overtime value (10 hours)?

 

[symbolipoint]

So one value for 40 hours, and one value for the overtime value (10 hours)?

YES. That is progress in understanding.

You are working for the sum of the money earned in the regular 40 hours AND the money earned for the 10 hours of overtime. Note that the total time is 50 hours. The SUM you seek is about MONEY.

 

[chiro]

So one value for 40 hours, and one value for the overtime value (10 hours)?

BadFish hi there. Like you I have a mental illness but not as severe with learning.

In terms of your question you have to understand multiplication and addition at the core. Once you understand these concepts you will be able to think about what mathematics means and why it is such a powerful tool in modern society.

First of all let's consider multiplication.

Let a = b x c

Now this means I have c lots of b or b lots of c. So we could say in our pay example that if we had 40 lots of hours and each hour is worth $15 then we have a = 40 x $15 = $600. Note that a is just a variable. I could have e = b x c but it wouldn't make a difference to the resulting equation.

Now we move to the concept of addition. When we add things together we collect like quantities together so that they are collected.

Lets say we have a box of apples with 20 per box and a bag of apples at 5 per bag. If I have one box and one bag I have a = 20 + 5 = 25 apples. Now these don't just represent apples they can be anything you want but remember that addition of two things that are the same variable just add as if you were counting them.

If we have say apples and oranges though and we added them together we can't simply
add the apple count to the orange count because they are different variables. Let's say
we represent the total amount T and apples to be A and oranges to be O. Then we have
T = A + O. Now because apples are apples and oranges are oranges we can't just add apples
to oranges and get one combined answer. We have to leave our answer in terms of A apples AND O oranges.

Now to your pay question. This is simply using the concepts I described of multiplication and
addition.

The first thing we do when looking at this problem is we start off by asking ourself how do we break down the problem?

In this case you know that you have two lots of pay amounts - one normal and one overtime. Since both are in dollars we will get one answer when we add both the overtime
amount to the normal amount which will represent the total amount that person will earn.

So we start off by saying that the overtime is 1.5 times the normal rate and the normal rate is 10$ per hour. In saying this let's say normal hours are 40 hours a week and overtime is
10 hours a week.

We start off by breaking up the problem into normal pay and overtime pay. Forget trying to remember a formula, but instead think of it in this way:

- Normal pay
= Number of hours x rate in dollars per hour
= 40 hours x 10 dollars per hour
= 400 dollars

- Overtime pay
= Number of hours x overtime rate in dollars per hour
= 10 hours x 10 dollars per hour x 1.5 [because our rate is 1.5 times the normal rate]
= 150 dollars

Now we have two separate amounts: one for normal, another for overtime which can be added together. Remember that the concept of addition says that if we have one set of
things and another set of things where both things are the same type of thing, then we simply have the total being the count of both things.

I hope that helps.

 

[BadFish]

BadFish hi there. Like you I have a mental illness but not as severe with learning.

In terms of your question you have to understand multiplication and addition at the core. Once you understand these concepts you will be able to think about what mathematics means and why it is such a powerful tool in modern society.

First of all let's consider multiplication.

Let a = b x c

Now this means I have c lots of b or b lots of c. So we could say in our pay example that if we had 40 lots of hours and each hour is worth $15 then we have a = 40 x $15 = $600. Note that a is just a variable. I could have e = b x c but it wouldn't make a difference to the resulting equation.

Now we move to the concept of addition. When we add things together we collect like quantities together so that they are collected.

Lets say we have a box of apples with 20 per box and a bag of apples at 5 per bag. If I have one box and one bag I have a = 20 + 5 = 25 apples. Now these don't just represent apples they can be anything you want but remember that addition of two things that are the same variable just add as if you were counting them.

If we have say apples and oranges though and we added them together we can't simply
add the apple count to the orange count because they are different variables. Let's say
we represent the total amount T and apples to be A and oranges to be O. Then we have
T = A + O. Now because apples are apples and oranges are oranges we can't just add apples
to oranges and get one combined answer. We have to leave our answer in terms of A apples AND O oranges.

Now to your pay question. This is simply using the concepts I described of multiplication and
addition.

The first thing we do when looking at this problem is we start off by asking ourself how do we break down the problem?

In this case you know that you have two lots of pay amounts - one normal and one overtime. Since both are in dollars we will get one answer when we add both the overtime
amount to the normal amount which will represent the total amount that person will earn.

So we start off by saying that the overtime is 1.5 times the normal rate and the normal rate is 10$ per hour. In saying this let's say normal hours are 40 hours a week and overtime is
10 hours a week.

We start off by breaking up the problem into normal pay and overtime pay. Forget trying to remember a formula, but instead think of it in this way:

- Normal pay
= Number of hours x rate in dollars per hour
= 40 hours x 10 dollars per hour
= 400 dollars

- Overtime pay
= Number of hours x overtime rate in dollars per hour
= 10 hours x 10 dollars per hour x 1.5 [because our rate is 1.5 times the normal rate]
= 150 dollars

Now we have two separate amounts: one for normal, another for overtime which can be added together. Remember that the concept of addition says that if we have one set of
things and another set of things where both things are the same type of thing, then we simply have the total being the count of both things.

I hope that helps.

Find the sum of pay when working $10 per hour for 40 hours, with the rate of 1.5x the normal rate for the extra 10 hours, for a total of 50 hours

h = hours
40 * 10h + 10 * 10h * 1.5 = $550
(Number of hours times 10 dollars per hour) + (overtime hours, 10 + $10 per hour * the overtime rate)

Is this right?

 

[Mark44]

Find the sum of pay when working $10 per hour for 40 hours, with the rate of 1.5x the normal rate for the extra 10 hours, for a total of 50 hours

h = hours
40 * 10h + 10 * 10h * 1.5 = $550
(Number of hours times 10 dollars per hour) + (overtime hours, 10 + $10 per hour * the overtime rate)

Is this right?

Yes, but I was confused at first. The usual abbreviation for hours is hr or hrs. I mistook your h to be a variable.

OK, we've beat the one with fixed numbers to death. Now can you work the somewhat more abstract problem that I posed several threads back?

An employee works h hours in a week, and is paid $10 per hour. What is the employee's gross pay for the week? You need two formulas.

 

[symbolipoint]

BadFish,
After rereading some of the earlier posts on this thread, the exact nature of your learning-problem is not clear; I thought someone mentioned that you are stricken with a form of Asperger's Syndrome, but I did not see this mentioned specificly in the earlier posts.
In any case, one may wonder if the actual nature of your book, Algebra the Easy Way, written in medieval story-like manner is actually an obstacke to learning? You wrote that you did very well in Algebra in middle school, but you are having trouble understanding now. Maybe, consider changing books? Use a more traditional book, even if the book is 20 or 30 years old. Used books are sometimes very easy to find, and for very low prices. The old, traditional books require the student to think critically, and let the Mathematics speak for itself; these books are less wordy than what you may currently be using; less words are less distracting. For Beginning Algebra, an older style book might be easier for you to learn from --- just a guess.

 

[BadFish]

BadFish,
After rereading some of the earlier posts on this thread, the exact nature of your learning-problem is not clear; I thought someone mentioned that you are stricken with a form of Asperger's Syndrome, but I did not see this mentioned specificly in the earlier posts.
In any case, one may wonder if the actual nature of your book, Algebra the Easy Way, written in medieval story-like manner is actually an obstacke to learning? You wrote that you did very well in Algebra in middle school, but you are having trouble understanding now. Maybe, consider changing books? Use a more traditional book, even if the book is 20 or 30 years old. Used books are sometimes very easy to find, and for very low prices. The old, traditional books require the student to think critically, and let the Mathematics speak for itself; these books are less wordy than what you may currently be using; less words are less distracting. For Beginning Algebra, an older style book might be easier for you to learn from --- just a guess.

I did very good in algebra in high school, did not do good in geometry in middle school. I have (at least some think so) a minor form of autism called asperger's. I was one of the best in my class in high school in algebra I, and was a math tutor, ironically, at the charter school. It's been many years since I graduated and the main difference was having a teacher around to show me, it makes all the difference. I do well in classrooms with teachers, I do *not* learn well from books. This is across the board, I also have other hobbies such as sleight of hand (magic) with coins which many books such as Bobo's Modern coin magic and for cards, Erdnase is written. I have trouble learning from these books too, understanding the wording and what it means. I do fine on DVD's, but books is something else. I was in special ed english but normal math class...
I feel so stupid right now I can't understand this book.
But I appreciate everyone's patience, if there's one thing I have it's persistence and determination, this isn't going to stop me from learning algebra and beyond.

 

[BadFish]

Yes, but I was confused at first. The usual abbreviation for hours is hr or hrs. I mistook your h to be a variable.

OK, we've beat the one with fixed numbers to death. Now can you work the somewhat more abstract problem that I posed several threads back?

An employee works h hours in a week, and is paid $10 per hour. What is the employee's gross pay for the week? You need two formulas.

$10/hour * h = Gross pay

I know you said you need 2 formulas, but why?

Example
$10 per hour * h (hours in a week)
Say h = 40
$10/per hour * (40)

Can you give me a clue?

 

[symbolipoint]

The clue is that 'h' is a variable. According the the problem description, any time exceeding 40 hours is paid at "time and a half".

Back to your reply in #52, maybe you are using a book not suited to you. Try a traditional Algebra 1 book instead. If you learned Algebra 1 well once, you only have reason to be able to relearn it BETTER than before; not worse than before. Good traditional books are written to express exactly what the author intends to express; no fancy literary tricks. Even so, you usually need to reread several passages many many times and think.
---Hey! I had trouble with high school English, too, when I was in high school; same with social studies. Most of the Mathematics courses were different.

 

[BadFish]

So, we need one formula for the normal rate of pay, (40 hours in a week), and another formula for the overtime pay, 10 hours a weeK?

 

[Ouabache]

So, we need one formula for the normal rate of pay, (40 hours in a week), and another formula for the overtime pay, 10 hours a weeK?

They may be combined into a single equation. Both parts look something like the general form you told me:
Pay = p ($)
Normal Rate of pay = r ($/hr)
time worked = t (hrs)
we chose t rather than h here for a more general construct, since time worked, may be given in weeks, months, etc..
also ( ) indicates the units of the variable

P = r * t

since you are now expecting two parts, one for normal pay and one for overtime pay, you might choose variables r1 and t1 for normal pay and r2 and t2 for overtime pay and the combined form can be:

P = (r1 * t1)+ (r2 * t2)

With the information that you have learned in the practice example, you have enough information to determine
r1 & r2, t1 & t2 in terms of r and t (hint: or a constant)

 

[BadFish]

P = (r1 * t1) + (r2 * t2)

$550 = (10/per hour * 40) + ($15 per hour * 10)

 

[Mark44]

No, you won't get a specific dollar amount.

Ouabache and I took slightly different tacks, where I was asking for two formulas, and he have one formula with two parts.

Let's go with a variation of his formula, with the t variables replaced by h variables -- all of our times are going to be in hours -- and with constants for the regular and overtime pay rates. Note that for the overtime calculation you can multiply the overtime hours by 1.5 OR you can multiply the pay rate by 1.5 (but not both).

P =10*h1 + 15*h2
Here h1 and h2 are the "regular" hours and overtime hours, respectively.

For the problem I posed, where an employee works H hours, at $10 per hour, what's the gross pay for this employee? Your answer should be an expression, not a constant. And there is one question you should ask before you give your answer.

 

[BadFish]

$10/per hour * h = gross pay

 

[BadFish]

No, you won't get a specific dollar amount.

Ouabache and I took slightly different tacks, where I was asking for two formulas, and he have one formula with two parts.

Let's go with a variation of his formula, with the t variables replaced by h variables -- all of our times are going to be in hours -- and with constants for the regular and overtime pay rates. Note that for the overtime calculation you can multiply the overtime hours by 1.5 OR you can multiply the pay rate by 1.5 (but not both).

P =10*h1 + 15*h2
Here h1 and h2 are the "regular" hours and overtime hours, respectively.

For the problem I posed, where an employee works H hours, at $10 per hour, what's the gross pay for this employee? Your answer should be an expression, not a constant. And there is one question you should ask before you give your answer.

Ahh, I see. I was supposed to write it in algebra format.

That makes sense

Let's say p = $550, then
P= 10*(40) + 15(the overtime rate)*10

To get the overtime rate multiply 1.5 x 10 (the normal rate)

 

[Ouabache]

P = (r1 * t1) + (r2 * t2)

$550 = (10/per hour * 40) + ($15 per hour * 10)

As Mark44 mentioned, we are looking for an expression(s), not specific values.
Yes we could have 2 equations with condition on each.
This is actually very useful for the general case, where work is anywhere from 1hr up to some large number.

For your original question:

Calculate your pay if you work more than 40 hours and are paid time and one half for every hour past 40.

for example:
P - pay ($)
r - normal rate of pay ($/hr)
t - time worked (hr)

equ. (1) P = r * t ; amount of pay working < or = 40 hrs
equ. (2) P = (3/2)r * t; amount pay for "only" time worked > 40hrs
Total Pay is sum of equ. (1) and (2)

For your example, we are given the person is working more than 40 hrs.
I suggested we could write this in a combined expression of the form:

equ. (3) P = (r1 * t1) + (r2 * t2)

here are the values I was hoping you would determine from our disussion:
r1 = r (the normal pay rate)
t1 = 40 (maximum normal number of hours)
r2 = (3/2) * r (time and a half; one and half times normal rate)
t2 = t-40 (the number of hours over 40 that have been worked)

Substituting those terms into the combined equation (3)
and you have valid solution to this problem, written in terms of the original r and t.

 

[Mark44]

Ahh, I see. I was supposed to write it in algebra format.

That makes sense

Let's say p = $550, then
P= 10*(40) + 15(the overtime rate)*10

To get the overtime rate multiply 1.5 x 10 (the normal rate)

No, let's not say that P = $550. You are starting with what you assume to be the answer, and as I said before, your answer will not be a specific number.

If the employee works H hours at $10/hour, what is the employee's gross pay?

You need to take into account whether the employee worked overtime hours, and your two formulas should produce algebraic expressions, not numbers, that reflect two situations.