Question

Acme Inc. spent $810 less on postage than on supplies. The ratio of postage costs to supply costs was 2 to 5. How much did Acme spend on postage? Solve this problem using algebra.

Answer 1

$540

p = postage
s = supplies

You spend 810 less on postage, so

p = s - 810

The 2nd equation is a ratio

$\frac{2}{5} = \frac{p}{s}$

But with cross multiplication, that becomes

2s = 5p

You are then left with the system of equations:

2s = 5p

p = s - 810

You can change the second equation so it becomes

p + 810 = s

and substitute it in for s in the first equation, so you get

2(p + 810) = 5p

2p + 1620 = 5p

1620 = 3p

540 = p

To check it, you can get money spent on supplies by adding 810, which gets 1350, which is indeed makes a 2:5 ratio between postage money and supply money