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.
