Rational Expression word problem

In summary, Nancy's lawn care specializes in residential lawn cutting and fertilizing. Nancy the owner has tracked her income and expenses. She has determined that her profit can be represented by the expression $5A, where A is the area of the lawn in square metres. The time in hours that it takes her to maintain a lawn is approximately 0.05A + 0.25.
  • #1
Pikachu1
8
0
Nancy's lawn care specializes in residential lawn cutting and fertilizing. Nancy the owner has tracked her income and expenses. She has determined that her profit can be represented by the expression $5A, where A is the area of the lawn in square metres. The time in hours that it takes her to maintain a lawn is approximately 0.05A + 0.25.

Write a rational expression for nancy profit per hour.
Evaluate the expression for a yard with an area of 90m^2Obviously there is some sort of formula for this that i don't understand.
 
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  • #2
When you see the word "per" (which means "for each"), as in miles per hour (or profit per hour), this means you want to take some total and divide by the number of hours. You are given both the total profit, and the number of hours, both as a function of $A$. Can you now construct a profit per hour function $P_h$ for Nancy?

\(\displaystyle P_h(A)=\frac{\text{Total profit}}{\text{hours to maintain a lawn}}=?\)
 
  • #3
MarkFL said:
When you see the word "per" (which means "for each"), as in miles per hour (or profit per hour), this means you want to take some total and divide by the number of hours. You are given both the total profit, and the number of hours, both as a function of $A$. Can you now construct a profit per hour function $P_h$ for Nancy?

\(\displaystyle P_h(A)=\frac{\text{Total profit}}{\text{hours to maintain a lawn}}=?\)
So it would be,

Ph(A) =$5A/ 0.05A + 0.25 ?

I feel like i am still missing something.
 
  • #4
Pikachu said:
So it would be,

Ph(A) =$5A/ 0.05A + 0.25 ?

I feel like i am still missing something.

I would just recognize that the units of the function are dollars per hour, and if using plain text, use bracketing symbols to indicate clearly what the denominator is as follows:

P_h(A) = 5A/(0.05A + 0.25)

So, for part b), you need to evaluate P_h(90). :D
 
  • #5
MarkFL said:
I would just recognize that the units of the function are dollars per hour, and if using plain text, use bracketing symbols to indicate clearly what the denominator is as follows:

P_h(A) = 5A/(0.05A + 0.25)

So, for part b), you need to evaluate P_h(90). :D

So, it would be? I have no idea why this question stomped me like that.
P_h(90) = 5(90)/0.05(90) +0.25 ?
 
  • #6
Pikachu said:
So, it would be? I have no idea why this question stomped me like that.
P_h(90) = 5(90)/0.05(90) +0.25 ?

Well, you really need bracketing symbols...

P_h(90) = 5(90)/(0.05(90) + 0.25)

The way you write it means:

\(\displaystyle P_h(90)=\frac{5(90)}{0.05(90)}+0.25\)

But what you want is:

\(\displaystyle P_h(90)=\frac{5(90)}{0.05(90)+0.25}\)

And the parentheses makes the meaning clear. :D
 
  • #7
MarkFL said:
Well, you really need bracketing symbols...

P_h(90) = 5(90)/(0.05(90) + 0.25)

The way you write it means:

\(\displaystyle P_h(90)=\frac{5(90)}{0.05(90)}+0.25\)

But what you want is:

\(\displaystyle P_h(90)=\frac{5(90)}{0.05(90)+0.25}\)

And the parentheses makes the meaning clear. :D

Thank you! I understand now.
You rock
 

FAQ: Rational Expression word problem

What is a rational expression?

A rational expression is a mathematical expression that contains a ratio of two polynomial expressions. It can be written in the form of p(x)/q(x), where p(x) and q(x) are polynomial expressions and q(x) is not equal to zero.

How do I solve a rational expression word problem?

To solve a rational expression word problem, you first need to identify the given information and determine what variables represent. Then, set up the expression using the given information and simplify it by factoring, canceling out common factors, and finding a common denominator. Finally, solve for the variable by isolating it on one side of the equation.

What are some common applications of rational expressions?

Rational expressions are commonly used in real-life situations involving proportions, rates, and scaling. For example, they can be used to calculate the speed of an object, determine the correct dosage of a medication, or calculate the amount of ingredients needed for a recipe.

How do I know if a rational expression is undefined?

A rational expression is undefined when the denominator is equal to zero. This is because division by zero is undefined in mathematics. When solving a rational expression, you need to check for any values of the variable that would make the denominator zero and exclude them from the solution.

Can I simplify a rational expression?

Yes, you can simplify a rational expression by factoring the numerator and denominator and canceling out common factors. This can help make the expression easier to work with and can also help identify any restrictions on the variable. However, not all rational expressions can be simplified, so it's important to check for any restrictions before simplifying.

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