Question

Maura is 5 years younger than her sister Cara. Seven years ago, Maura was half as old as her sister. How old is Maura now?

Answer 1

Let's call Maura's age now M and Cara's age now C.

We know Maura is five years younger than Cara. In symbols that is, M - 5 = C

We also know that 7 years ago Maura's age was half of Cara's. Maura's age 7 years ago was M-7 and Cara's age seven years ago was C-7. Since Maura's age (7 years ago) was half of Cara's we can write in symbols: $M-7= \frac{1}{2}(C-7)$

Let's take that last equation and substitute C - 5 for M (this is because according to our first equation these are equal). When we do this we get an equation with only C as the variable and solve for C as follows:

$M-7= \frac{1}{2}(C-7)$
$C-5-7= \frac{1}{2}(C-7)$
$C-12= \frac{1}{2}C-( \frac{1}{2})(7)$
$C-12= .5C-3.5$
$.5C-12= -3.5$
$.5C= 8.5$
$C= 17$

Cara is 17. Since Maura is 5 years younger she is 12.

As a check, seven years ago Cara was 10 and Maura was 5. It is the case that Maura was half Cara's age seven years ago.