Michael is 12 years older than Brandon. Seventeen years ago, Michael was 4 times as old as Brandon. How is Brandon now?

Question

i dont know how to find the answer. 

Answer 1

Hi Jose.

 

To start this problem, you need a way to represent each person.  So we will let Michael be "m" and Brandon be "b".

 

Now just turn their words into math operations.

 

"Michael is 12 years older than Brandon" translates to m = 12 + b

"17 years ago, Michael was 4 times as old as Brandon"  17 years ago is 17 years ago for both Michael and Brandon, so that part is (m-17)  and (b-17).  So the 17-years earlier Michael (m-17) = 4 * the 17-years-earlier Brandon (b-17).

 

Or, the second part gives us  m-17 = 4(b-17)

If we add 17 to both sides, we can isolate the "m" and get  

 

m=17 + 4(b-17)

 

Distribute the 4 into (b-17) and get m=17 + 4b - 68

 

Then combine like terms on the right and get  m = 4b-51

This equation along with the first equation:  m=12 + b

can be combined.  Since m always equals m,  we can subsitute the bottom "m" into the top equation's "m".

 

12 + b = 4b - 51

 

Now solve for b

 

Subtract "b" from both sides.

 

12 = 3b - 51

 

Now add 51 to both sides

 

63 = 3b

 

Now divide both sides by 3

 

21 = b

 

 

So Brandon's age is 21 years old.

 

Since m = 12 + b, m= 12 + 21 = 33

 

So Michaels age is 33 years old.

 

 

Let's check.   Is Michael 12 years older than Brandon?  Brandon = 21 + 12 = 33 = Michael's age.  YES.

 

Michael 17 years ago was 33 - 17 = 16 years old.

Brandon 17 years ago was 21 - 17 =4 years old.

 

17 years ago, was Michael 4 times as old as Brandon?  Is Michael's age 17 years ago (16 years old)  four times Brandon's age 17 years ago (4 years old)?  YES!  So we got it right!

 

Final Answer:  Brandon is 21 years old.