Question

Sarah earns $525 more than Andrew each month. They spend $1250 a month and save the rest. Sarah does not have any savings at first. After 11 months she has $8250 in savings. How much does Andrew earn in a year?

Answer 1

Lets begin with the first sentence.  We will let S = Sarah's monthly earnings and A = Andrews.

S = A + 525 (since Sarah earns more than Andrew).

Then you are told they spend 1250 each month and save the rest.  The total savings will then be the difference times the number of months.

Savings per month (Sarah ) = S - 1250

Savings (Sarah Total) = (S - 1250)* number of months.

Plug in the number of months and total savings to figure out how much Sarah makes each month.

8250 = (S - 1250)*11

750 = S - 1250

S = 750 + 1250

S = 2000

From Sarah's earnings each month we can find Andrews (using the first equation).

2000 = A + 525

A = 2000 - 525

A = $1475

Finally you are asked for the yearly earnings:

12* $1475 = $17,700

Andrew earns $17,700 each year.