word problem

Question

Four years ago, Rosita was three times as old as Matias was. In three years, Rosita will be only two years less than twice as old as Matias will be. How old are they no

Answer 1

Let R = Rosita's age now

Let M = Matias' age now 

 

Four years ago Rosita was 3 times as old as Matias was  ==>  

(R - 4) = 3*(M - 4)  

 

In three years Rosita will be 2 years less than twice as old as Matias will be  ==>  

(R + 3) = 2*(M + 3) - 2

 

Solve each equation for R 

 

R = 3*M - 12 + 4 = 3*M - 8

R = 2*M + 6  - 2 - 3 = 2*M + 1

 

Set these 2 expressions for R equal to each other 

 

3*M - 8 = 2*M + 1

M = 9

 

Plug this in to the last equation for R = 2*9 + 1 = 19 

 

So Rosita is 19 now and Matias is 9 now 

 

Check:  4 years ago Rosita was 15 and Matias was 5, 15 = 3*5

            In 3 years Rosita will be 22 and Matias will be 12, 22 = 2*12 - 2