Question

abbie spent 5/8 of her money and saved the rest. if she spent 45,how much money did she have at first?

Answer 1

$72

Further explanation

Given:

Abbie spent ⁵/₈ of her money and saved the rest.

She spent $45.

Question:

How much money did she have at first?

The Process:

The meaning of "Abbie spent ⁵/₈ of her money" is that she has spent 5 of the 8 parts of the money she had at first.

Let us make a pattern of 8 units for the amount of money that Abbie had at first.

$\boxed{\cdot}\boxed{\cdot}\boxed{\cdot}\boxed{\cdot}\boxed{\cdot}\boxed{\cdot}\boxed{\cdot}\boxed{\cdot}$

Since Abbie spent ⁵/₈ of her money, then we create a pattern of 5 units containing $9 each. Recall that $\boxed{\ 45 \div 5 = \ 9}$

$\boxed{\ 9}\boxed{\ 9}\boxed{\ 9}\boxed{\ 9}\boxed{\ 9} = \ 45$

From the pattern above, we can see that $\boxed{ \ 1 \ unit = \ 9 \ }.$

Let us calculate how much money Abbie had at first.

$\boxed{ \ 1 \ unit = \ 9 \ }$

$\boxed{ \ 8 \ unit = \ ? \ }$

$\boxed{ \ 8 \times \ 9 = \ 72 \ }$

Thus, the money Abbie had at first is $72.

The complete pattern of Abbie's initial money is as follows:

$\boxed{\ 9}\boxed{\ 9}\boxed{\ 9}\boxed{\ 9}\boxed{\ 9}\boxed{\ 9}\boxed{\ 9}\boxed{\ 9} = \ 72$

- - - - - - - - - -

Quick Steps:

Let M as Abbie's initial money.

$\boxed{ \ \frac{5}{8} \times M = \ 45 \ }$

Both sides are multiplied by ⁸/₅ so that M is the subject alone on the left side.

$\boxed{ \ M = \frac{8}{5} \times \ 45 \ }$

We crossed out 5 and 45.

$\boxed{ \ M = 8 \times \ 9 \ }$

$\boxed{ \ M = \ 72 \ }$

Thus, the money Abbie had at first is $72.

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Keywords: Abbie, spent 5/8 of her money, saved the rest, $45, $72, how much money, she have at first, the pattern

Answer 2

Note that 5/8 is equivalent to $45

1/8 is equivalent to $45 ÷ 5 = 9

8/8 (aal) is equivalent to 8 x 9 = 72

She had $72