SOLUTION: Sarah has $20 more than Frank, but $40 less than Bruce. If Bruce has $10 more than two times what Frank has, write an equation to find how much money each person has.

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Sarah has $20 more than Frank, but $40 less than Bruce. If Bruce has $10 more than two times what Frank has, write an equation to find how much money each person has.      Log On


   

Question 979850: Sarah has $20 more than Frank, but $40 less than Bruce. If Bruce has $10 more than two times what Frank has, write an equation to find how much money each person has.
Answer by 428225(90) About Me  (Show Source):
You can put this solution on YOUR website!
let the letters B, S and F represent the random variable of how much money Bruce, Sarah and Frank have.

S=F+20  (equation 1)
S=B-40 (equation 2)
B=2F+10 (equation 3)

substitute equation 1 into 2

F+20=B-40 (equation 4)

substitute equation 3 into 4 in order to get the equation in terms of F only

F+20=2F+10-40
F+20=2F-30
F=50

Sub the value of F=50 into equation 1 and 3 and you get: S=70 & B=110

Therefore, B=110, F=50, S=70