Answer :

Ryan2
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

$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.

[tex]\boxed{\cdot}\boxed{\cdot}\boxed{\cdot}\boxed{\cdot}\boxed{\cdot}\boxed{\cdot}\boxed{\cdot}\boxed{\cdot}[/tex]

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

[tex]\boxed{\$ 9}\boxed{\$ 9}\boxed{\$ 9}\boxed{\$ 9}\boxed{\$ 9} = \$ 45[/tex]

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

Let us calculate how much money Abbie had at first.

[tex]\boxed{ \ 1 \ unit = \$ 9 \ }[/tex]

[tex]\boxed{ \ 8 \ unit = \ ? \ }[/tex]

[tex]\boxed{ \ 8 \times \$ 9 = \$ 72 \ }[/tex]

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

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

[tex]\boxed{\$ 9}\boxed{\$ 9}\boxed{\$ 9}\boxed{\$ 9}\boxed{\$ 9}\boxed{\$ 9}\boxed{\$ 9}\boxed{\$ 9} = \$ 72[/tex]

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Quick Steps:

Let M as Abbie's initial money.

[tex]\boxed{ \ \frac{5}{8} \times M = \$ 45 \ }[/tex]

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

[tex]\boxed{ \ M = \frac{8}{5} \times \$ 45 \ }[/tex]

We crossed out 5 and 45.

[tex]\boxed{ \ M = 8 \times \$ 9 \ }[/tex]

[tex]\boxed{ \ M = \$ 72 \ }[/tex]

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