$72
Given:
Question:
How much money did she have at first?
The Process:
Let us design a diagram that matches the above situation.
[tex]\boxed{\cdot} \boxed{\cdot} \boxed{\cdot} \boxed{\cdot} \boxed{\cdot} \boxed{\cdot} \boxed{\cdot} \boxed{\cdot}[/tex]
1 unit represents 1 part of all the money she had at first.
Abbie spent [tex]\frac{5}{8}[/tex] of her money and saved the rest, that is [tex]\boxed{\cdot} \boxed{\cdot} \boxed{\cdot} \boxed{\cdot} \boxed{\cdot} [/tex] or 5 of 8 units.
From the diagram she spent above, 5 units exactly match the $ 45 she spent.
[tex]\boxed{ \ 5 \ units = \$ 45 \ }[/tex]
[tex]\boxed{ \ 1 \ unit = \$ \ ? \ }[/tex]
[tex]\boxed{ \ \$ 45 \div 5 \ units = \$ 9 \ }[/tex]
Therefore, [tex]\boxed{ \ 1 \ unit = \$ 9 \ }[/tex]
Abbie had 8 units at first.
Let's count how much money did she have at first.
[tex]\boxed{ \ 1 \ unit = \$ 9 \ }[/tex]
[tex]\boxed{ \ 8 \ unit = \$ \ ? \ }[/tex]
[tex]\boxed{ \ = 8 \times 9 \ }[/tex]
[tex]\boxed{\boxed{ \ \$ 72 \ }}[/tex]
Thus, she had $ 72 at first.
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Quick Steps
[tex]\frac{5}{8}[/tex] of her money at first is $45.
The money she had at first is
[tex]\boxed{ \ \$ 45 \div \frac{5}{8} = \ ? \ }[/tex]
[tex]\boxed{ \ = \$ 45 \times \frac{8}{5} \ }[/tex]
We crossed out 45 and 5.
[tex]\boxed{ \ = \$ 9 \times \frac{8}{1} \ }[/tex]
[tex]\boxed{\boxed{ \ \$ 72 \ }}[/tex]
Keywords: Abbie spent, 5/8 of her money, and, saved the rest, if, she spent, $45, how much, she have at first, diagram, unit, part
