Helen spent 3/8 of her money at the first store she visited. She then spent 3/4 of her remaining money at the second store. If Helen had $20 left, how much money did she start with?

Question

7525 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-12-06T00:40:14

$$ 128$ $$128$

After spending $\frac{3}{8}$ $3/8$ of the money, Helen had $\frac{5}{8}$ $5/8$ left.

Then she spent $\frac{3}{4}$ $3/4$ of the remaining $\frac{5}{8}$ $5/8$ .

That would mean by the time she is done, she'd have $\frac{1}{4}$ $1/4$ of $\frac{5}{8}$ $5/8$ left

$\frac{1}{4} \times \frac{5}{8} = \frac{5}{32}$ $1/4 times 5/8 = 5/32$

we know that the money she had left was $$ 20$ $$20$

Therefore $$ 20 = \frac{5}{32}$ $$20 = 5/32$

The amount of money Helen started with would be equal to
$\frac{32}{32}$ $32/32$ $= \frac{1}{1}$ $= 1/1$ because that is 100%, it's all of her money

There are multiple ways to reach $\frac{32}{32}$ $32/32$ with algebra. Here's one way:

Multiply both sides of ' $$ 20 = \frac{5}{32}$ $$20 = 5/32$ ' by 32

That gives $$ 640 = 5$ $$640 = 5$

Now divide both sides by 5

This gives $$ 128 = 1$ $$128 = 1$

The $1$ $1$ represents the fraction of money she has, meaning that 1 is the total amount.