Answer:

Martin will be 30 years old

Step-by-step explanation:

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ALGEBRA SIMULTANEOUS EQUATIONS

Dozer R. asked • 06/14/18

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.

I'm kinda confused about this question..I think its a simultaneous equation

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Mark B. answered • 06/14/18

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PhD Candidate and Algebra I Tutor with 20 Years of Experience

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Good Morning, Dozer,

How about we do this?

Let Luther's age be x and Martin's age be 4x. This is their respective ages currently.

Then:

According to the problem, after 10 years the age of Luther will be (x + 10) and the age of Martin will be 4x + 10. All we did here was express what was stated in the problem using x for Luther and 4x for Martin and adding 10, right?

Therefore:

4 x + 10 = 2 (x + 10)

Why? Because after 10 years Martin "will be twice the age of his brother."

Now solve the above equation for x, okay?

4x + 10 = 2 (x + 10)

4 x + 10 = 2 x + 20

4x - 2x = 20 - 10

2x = 10

x = 5

Remember, we said Luther would be represented by x, right? Therefore, Luther is 5. Martin, is represented by 4x, right?

Therefore, Martin is 4(5) or 20

Luther is 5

Martin is 20

Now, let's check our work, okay?

We must meet two conditions according to our problem:

First, Martin must be four times as old as his brother currently or at present. 5 * 4 is in fact, 20. Check.

Second, after 10 years Martin needs to be twice the age of Luther, right? In 10 years Luther will be 15, and Martin will be 30. Check.