Question

Three friends are trying to raise money for a school fundraiser. Jack was able to collect $15.75 more than Horacio. Rashad collected a third as much money as Horacio. Together, the boys collected a total of $126.35. How much money did each friend collect for the fundraiser? Write and solve an equation to find your solution. Identify the if-then moves used when solving the equation.

Answer 1

Explanation:

Let the money raised by Horacio be x

The money raised by Rashad = (1/3)*x

The money raised by Jack = x + 15.75

Total money raised by three friends = $ 126.35

`x+(1)/(3)x+x+15.75=126.35\\\\2x+(1)/(3)x+15.75=126.35\\\\(7)/(3)x+15.75=126.35\\\\(7)/(3)x=126.35-15.75\\\\(7)/(3)x=110.60\\\\x=110.60*(3)/(7)\\\\x=15.80*3`

x = $ 47.40

The money raised by Horacio =$47.40

The money raised by Jack = 47.40 + 15.75 = $63 .15

The money raised by Rashad = 47.40/3 = $ 15.80

Answer 2

h = $47.40, j = $63.15, r = $15.80

Explanation:

This a systems of equation problem:

j + h + r = 126.35 (how much the boys raised together)

j = 15.75 + h (if Horacio had 15.75 more, then the boys would be equal)

h = 3r (if Rashad tripled his money, then he and Horacio would by equal)

You need to use substitution to find how much one boy made, then plug it into the other equations. Let's solver for Horacio first.

(15.75 + h) + h + (h/3) = 126.35

7h/3 = 110.6, 7h = 331.8

h = $47.40

j = 15.75 + 47.40, j = $63.15

47.40 = 3r, r = $15.80

Double check by adding of the prices together:

$47.40 + $63.15 + $15.80 = $126.35