How Old Is Tanya in This Age Problem?

[harpazo]

Homework Statement

Find Tanya's present age by setting up a system of equations and using the substitution method.

Relevant Equations

T = M + 28
T + 6 = 3(M + 6)

Tanya is 28 years older than Marcus. In 6 years, Tanya will be three times as old as Marcus. How old is Tanya now?

Let T = Tanya

Let M = Marcus

Set Up:

T = M + 28...Equation A
T + 6 = 3(M + 6)...Equation B

Solve Equation A for M.

T = M + 28

T - 28 = M

Substitute T - 28 into Equation B.

T + 28 = 3(T - 28 + 6)

T + 28 = 3(T - 22)

T + 28 = 3T - 66

T - 3T = -66 - 28

-2T = -94

T = -94/-2

T = 47

Tanya is 47 years old.

What about checking the answer? I need to find M first.

Let T = 47

T = M + 28

47 = M + 28

47 - 28 = M

19 = M

Marcus is 19 years old.

Is 47 > 19 by 28?

Well, 19 + 28 = 47.

I conclude that Tanya is 47 years old.

 

[mjc123]

It doesn't satisfy equation B. When you wrote
T + 28 = 3(T - 28 + 6)
you should have written
T + 6 = 3(T - 28 + 6)

 

[PeroK]

Homework Statement:: Find Tanya's present age by setting up a system of equations and using the substitution method.
Relevant Equations:: T = M + 28
T + 6 = 3(M + 6)

Tanya is 28 years older than Marcus. In 6 years, Tanya will be three times as old as Marcus. How old is Tanya now?

I conclude that Tanya is 47 years old.

In six years Tanya will be 53, which isn't three times any whole number. That answer cannot possibly be right.

 

[vela]

Tanya is 47 years old.

What about checking the answer? I need to find M first.

Let T = 47
T = M + 28
47 = M + 28
47 - 28 = M
19 = M

Marcus is 19 years old.

Is 47 > 19 by 28?

Well, 19 + 28 = 47.

Considering you solved for M by subtracting 28 from T, it shouldn't be a surprise that you found M+28 = T, so this wasn't much of a check for the correctness of your solution. Generally, as @mjc123 pointed out, you need to check all of the conditions to verify that a solution is correct.

Note that you set the problem up correctly, which is usually the hard part. You just made a mistake in solving the system of equations. One method I found helpful to avoid simple mistakes is when I write a line down, I try to clear my mind, repeat that step, and make sure I get the same thing. If I don't, I figure out which one is correct (if either) and what the error was in obtaining the other. Catching mistakes as you go along is a lot easier than reaching the end and then going back to try find the error in all of the work.

 

[harpazo]

Considering you solved for M by subtracting 28 from T, it shouldn't be a surprise that you found M+28 = T, so this wasn't much of a check for the correctness of your solution. Generally, as @mjc123 pointed out, you need to check all of the conditions to verify that a solution is correct.

Note that you set the problem up correctly, which is usually the hard part. You just made a mistake in solving the system of equations. One method I found helpful to avoid simple mistakes is when I write a line down, I try to clear my mind, repeat that step, and make sure I get the same thing. If I don't, I figure out which one is correct (if either) and what the error was in obtaining the other. Catching mistakes as you go along is a lot easier than reaching the end and then going back to try find the error in all of the work.

I will try again.

 

[vela]

Did you redo the work or are you sticking with T=47? If it's the latter, that's the wrong answer as explained by the others.

One thing I tell my students is that there are tons of ways of doing a problem incorrectly and relatively few ways to do it correctly, so the odds are in favor of them making a mistake. Hence, being able to avoid errors in the first place and to be able to detect and find mistakes are invaluable skills to develop.

 

[FactChecker]

I got the right answer. Good enough for me.

Really? T=47 => M=47-28 (Equation A) = 19?
So T + 6 = 3(M + 6) (Equation B)
53 = 3*(19+6) = 3*25 = 75
53=75?

 

[DaveC426913]

T = M + 28...Equation A
T + 6 = 3(M + 6)...Equation B

...

Substitute T - 28 into Equation B.

T + 28 = 3(T - 28 + 6)

Yeah. Bit of a mix up there at the "T+28 = "Ultimately, you have over-calculated Tanya's age by 13 years. Tanya is not amused.

 

[harpazo]

Did you redo the work or are you sticking with T=47? If it's the latter, that's the wrong answer as explained by the others.

One thing I tell my students is that there are tons of ways of doing a problem incorrectly and relatively few ways to do it correctly, so the odds are in favor of them making a mistake. Hence, being able to avoid errors in the first place and to be able to detect and find mistakes are invaluable skills to develop.

I am going to do the math again.

 

[harpazo]

Yeah. Bit of a mix up there at the "T+28 = "Ultimately, you have over-calculated Tanya's age by 13 years. Tanya is not amused.

T = M + 28...Equation A
T + 6 = 3(M + 6)...Equation B

M + 28 + 6 = 3M + 18

M + 34 = 3M + 18

M - 3M = 18 - 34

-2M = -16

M = -16/-2

M = 8

Marcus is 8.

T = M + 28

T = 8 + 28

T = 36

Tanya is 36 years old.

 

[FactChecker]

Looks good. You should get the habit of going to the original statements and making sure that your answers work in every statement.

 

[harpazo]

Looks good. You should get the habit of going to the original statements and making sure that your answers work in every statement.

I will continue with age word problems tomorrow as well. More practice is required. As you can clearly see, all age applications posted have been fairly easy. Made a few typos and silly algebra errors. Other than that, I feel confident about my threads today.

 

[DaveC426913]

I will continue with age word problems tomorrow as well. More practice is required. As you can clearly see, all age applications posted have been fairly easy. Made a few typos and silly algebra errors. Other than that, I feel confident about my threads today.

Good plan. I recall from my school math days that almost all marks I lost were due to absent-minded typos and other easily avoidable mistakes. It was only occasionally that I made an actual conceptual error.

Double check your work. Don't rush. Try working from solution back to source to see if it jives.
If you're like me, those simple things make a difference of 10-20% in your grades.