$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 @@MATH_TOKEN_1@@
@@MATH_TOKEN_2@@
From the pattern above, we can see that @@MATH_TOKEN_3@@
Let us calculate how much money Abbie had at first.
@@MATH_TOKEN_4@@
@@MATH_TOKEN_5@@
@@MATH_TOKEN_6@@
Thus, the money Abbie had at first is $72.
The complete pattern of Abbie's initial money is as follows:
\(\boxed{\$ 9}\boxed{\$ 9}\boxed{\$ 9}\boxed{\$ 9}\boxed{\$ 9}\boxed{\$ 9}\boxed{\$ 9}\boxed{\$ 9} = \$ 72\)
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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.
Learn more
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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
