Mavis is 5 years older than her brother. Five years ago she was 2 times older than her brother. How old is each person?

Question

Mavis is 5 years older than her brother. Five years ago she was 2 times older than her brother. How old is each person?

Answer 1

Hi Gia,

 

Setting up the problem is critical to solving it. This  problem requires two equations to solve it.

 

First,

let m stand for Mavis and

let b stand for Mavis' brother

 

First equation

 

m = 5 + b

 

Second equation

let m-5 equal Mavis' age 5 years ago

let b-5 equal her bother's age 5 years ago

 

m - 5 = 2(b-5); distribute the 2

m-5 = 2b - 10; add 5 to both sides

 

m = 2b - 5

 

Set the equations equal to each other and solve for b

 

5 + b = 2b - 5; add 5 to both sides

10 + b = 2b; subtract b from both sides 

10 = b

 

So;

Mavis' brother is 10 and Mavis is 15 since 10 + 5 = 15

 

Check;

5 + b = 2b - 5; substitute 10 in for b

5 + 15 = 2(10) - 5; 

15 = 20 - 5

15 = 15

 

If Mavis is 15 and her brother is 10 five years ago they would be 10 and 5 respectively which means Mavis was 2 times older than her brother

 

I hope this was helpful,

 

Sincerely, 

Patrick S.

Answer 2

Let B be the brother's age today.  Let M be Mavis' age today.

 

What is true today?

 

Brother's age plus 5 years equals Mavis' age.

 

B + 5 = M.

 

 

What was true five years ago?

 

Brother was five years younger:  B - 5

 

Mavis was five years younger:  M - 5.

 

Mavis was twice as old as her brother:  2(B - 5) = M - 5.

 

 

Let's solve.

 

2(B - 5) = M - 5

 

B + 5 = M

 

Substitute the value of M from the second equation into the first.

 

2(B - 5) = B + 5 - 5

 

Simplify.

 

2B - 10 = B

 

B = 10

 

Go back and solve for M.

 

B + 5 = M

 

10 + 5 = M

 

M = 15.

 

Mavis is 15 years old now.  Her brother is 10 years old now.