Abbie spent \(\frac{5}{8}\) of her money and saved the rest. If she spent $45, how much money did she have at first?

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

Answered by Ryan2 | 2024-06-10

$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.
⋅ ​ ⋅ ​ ⋅ ​ ⋅ ​ ⋅ ​ ⋅ ​ ⋅ ​ ⋅ ​
Since Abbie spent ⁵/₈ of her money, then we create a pattern of 5 units containing $9 each. Recall that $45 ÷ 5 = $9 ​
$9 ​ $9 ​ $9 ​ $9 ​ $9 ​ = $45
From the pattern above, we can see that 1 u ni t = $9 ​ .
Let us calculate how much money Abbie had at first.
1 u ni t = $9 ​
8 u ni t = ? ​
8 × $9 = $72 ​
Thus, the money Abbie had at first is $72.
The complete pattern of Abbie's initial money is as follows:
$9 ​ $9 ​ $9 ​ $9 ​ $9 ​ $9 ​ $9 ​ $9 ​ = $72

Quick Steps:
Let M as Abbie's initial money.
8 5 ​ × M = $45 ​
Both sides are multiplied by ⁸/₅ so that M is the subject alone on the left side.
M = 5 8 ​ × $45 ​
We crossed out 5 and 45.
M = 8 × $9 ​
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

Answered by BladeRunner212 | 2024-06-12

Abbie had $72 at first. She spent 5/8 of her money, which equals $45. This confirms her initial amount by verifying the calculations.
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Answered by BladeRunner212 | 2024-10-13