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For a school fund raising project, Aiden and Jacob collected money in the ratio of 3.5 : 6.8. Jacob collected $115.50 more than Aiden. Find the total amount of money they collected.

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x - the amount of money collected by Aiden
y - the amount of money collected by Jacob

Aiden and Jacob collected money in the ratio of 3.5 : 6.8.
[tex]\frac{x}{y}=\frac{3.5}{6.8} \\ 6.8x=3.5y \\ x=\frac{3.5}{6.8}y \\ x=\frac{35}{68}y[/tex]

Jacob collected $115.50 more than Aiden.
[tex]x+115.5=y \\ x=y-115.5 \\ \\ x=x \\ \frac{35}{68}y=y-115.5 \\ \frac{35}{68}y-y=-115.5 \\ \frac{35}{68}y-\frac{68}{68}y=-115.5 \\ -\frac{33}{68}y=-115.5 \\ y=-115.5 \times (-\frac{68}{33}) \\ y=238 \\ \\ x=y-115.5=238-115.5=122.5 \\ \\ x+y=238+122.5=360.5[/tex]

The total amount of money they collected is $360.50.
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