Finding Present Ages: Solving a Two-Variable Linear Equation

[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 = LutherMartin 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 + 204L - 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]

Perfect method, correct answer.

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]

Perfect method, correct answer.

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.

 

[pbuk]

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.

 

[phinds]

@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).

 

[PeroK]

@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.

What's your best guess?

 

[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]

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 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.

What's your best guess?

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]

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.

 

[phinds]

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.

 

[phinds]

I will make some effort but try to understand that there are applications that throw students in for a loop. Sample: Probability Applications.

Just keep in mind the forum rule that we cannot give help unless you make at least some effort on you own. As I said, if you don't understand all/part of the question, ask about that. Do NOT just post a problem and then ask us to get you started (without having made any effort yourself and without saying what you find confusing).

 

[harpazo]

Just keep in mind the forum rule that we cannot give help unless you make at least some effort on you own. As I said, if you don't understand all/part of the question, ask about that. Do NOT just post a problem and then ask us to get you started (without having made any effort yourself and without saying what you find confusing).

I understand and concur.