# Find Their Present Ages

harpazo
Homework Statement:
Set up a system of equations to find the ages of Martin and his brother Luther.
Relevant Equations:
M = 4L
M + 10 = 2(L + 10)
Martin is four times as old as his brother Luther at present. After 10 years he will be twice the age of his brother. Find their present ages.

Let M = Martin

Let L = Luther

Martin is four times as old as his brother Luther at present.

M = 4L

After 10 years he will be twice the age of his brother.

M + 10 = 2(L + 10)

I came up with the following equations:

M = 4L...Equation A
M + 10 = 2(L + 10)...Equation B

I will now replace M in Equation B with 4L.

4L + 10 = 2(L + 10)

4L + 10 = 2L + 20

4L - 2L = 20 - 10

2L = 10

L = 10/2

L = 5

Luther is 5 years old.

Martin is 4 times Luther's age or 4(5) is 20 years old.

pbuk

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Now check them back to make sure (is Martin is four times as old as his brother Luther at present? After 10 years will he be twice the age of his brother?)

harpazo and FactChecker
harpazo

Now check them back to make sure (is Martin is four times as old as his brother Luther at present? After 10 years will he be twice the age of his brother?)
Well, 20 is 4 times greater than 5.

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Well, 20 is 4 times greater than 5.
Yes, and in 10 years?

Note that I'm not saying that your answer is wrong, just that checking back is an important part of succeeding with this kind of problem.

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@harpazo, I want to second what @pbuk said. It's very important that you learn to automatically check your work on such problems and once you do that you won't even have to ask anyone else if you are right, you will KNOW you are right (and if you're not, then you can rework the problem until you get an answer that checks out).

Vanadium 50, harpazo, SammyS and 2 others
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@harpazo here's a question. Without doing any further equations of calculations, what's the answer:

Martin is four times as old as his brother Luther at present. After 20 years he will be twice the age of his brother. Find their present ages.

harpazo
Yes, and in 10 years?

Note that I'm not saying that your answer is wrong, just that checking back is an important part of succeeding with this kind of problem.
In 10 years, Luther will be L + 10.

L = 5

In 10 years, Luther will be 15 years.

pbuk
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In 10 years, Luther will be L + 10.

L = 5

In 10 years, Luther will be 15 years.
... and Mike will be M + 10 = 30, which is consistent with "after 10 years he will be twice the age of his brother".

harpazo
harpazo
@harpazo here's a question. Without doing any further equations of calculations, what's the answer:

Martin is four times as old as his brother Luther at present. After 20 years he will be twice the age of his brother. Find their present ages.

After 10 years, Luther will be L + 10.

Let L = 5

Then 10 + 5 = 15.

After 10/after 20 = 15/L

20(15) = 10L

300 = 10L

300/10 = L

30 = L

After 20 years, Luther will be 30 years old.

harpazo
... and Mike will be M + 10 = 30, which is consistent with "after 10 years he will be twice the age of his brother".
More age word problems this weekend.

pbuk
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More age word problems this weekend.
We'll be looking for a correctly worked-through and back-checked answer first time now!

harpazo
... and Mike will be M + 10 = 30, which is consistent with "after 10 years he will be twice the age of his brother".
Cool.

harpazo
We'll be looking for a correctly worked-through and back-checked answer first time now!
I will not show work if the problem is fuzzy and I just don't know where to begin. Hopefully, this will not be for a while. I will post distance, coins, lever, geometry, trigonometry, financial and miscellaneous word problems as the weeks go by.

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I will not show work if ...
You are required to make some effort at problems. If you have trouble interpreting part of the problem statement, then ask about that specifically.

harpazo
We'll be looking for a correctly worked-through and back-checked answer first time now!
I will not show work if the problem is fuzzy and I just don't know where to begin. Hopefully, this will not be for a while. I will post distance, coins, lever, geometry, trigonometry,
You are required to make some effort at problems. If you have trouble interpreting part of the problem statement, then ask about that specifically.
I will make some effort but try to understand that there are applications that throw students in for a loop. Sample: Probability Applications.