SOLUTION: Bob, Sue, and Fred have $155 all together. Bob has $5 more than Sue and Fred together. If Sue gives Fred $5, he will have twice as much as she does. How much does each person have

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Bob, Sue, and Fred have $155 all together. Bob has $5 more than Sue and Fred together. If Sue gives Fred $5, he will have twice as much as she does. How much does each person have      Log On


   

Question 1170238: Bob, Sue, and Fred have $155 all together. Bob has $5 more than Sue and Fred together. If Sue gives Fred $5, he will have twice as much as she does. How much does each person have?

Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
system%28b%2Bx%2Bf=155%2Cb=x%2Bf%2B5%2Cf%2B5=2%28x-5%29%29

-
system%28b-x-f=5%2Cf%2B5=2x-10%29

system%28b-x-f=5%2Cf-2x=-15%29

system%28b-x-f=5%2Cf=2x-15%29

b-x-2x%2B15=5
b-3x=-10
b=3x-10
-
revise original system
system%283x-10%2Bx%2Bf=155%2C3x-10=x%2Bf%2B5%2Cf%2B5=2x-10%29
system%284x%2Bf=165%2C2x-f=15%29
%284x%2Bf%29%2B%282x-f%29=165%2B15
6x=180
highlight%28x=30%29-----------Sue had,
and you can find the other two values.

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


I definitely would NOT use three variables to solve the problem, as the other tutor did....!
Do some analysis of the problem to figure out how to set up and solve it with much less work. My suggestion....

(1) Since Bob had $5 more than Sue and Fred together, first divide the total $155 into two parts with one of them $5 more than the other. You can do that mentally (informally), or you can use basic algebra. That will give you $80 for Bob's share and $75 for Sue's and Fred's combined.

(2) Finding Sue's share and Fred's share is a bit more complicated, so formal algebra is probably a good way to go. (Of course, if the speed of getting an answer is important, good old trial and error will probably get you there faster.)

x = Sue's share
75-x = Fred's share

x-5 = Sue's share after giving Fred $5
80-x = Fred's share after getting $5 from Sue

At this point, Fred has twice as much as Sue:

80-x+=+2%28x-5%29
80-x+=+2x-10
90+=+3x
30+=+x

ANSWERS:
Bob: $80
Sue: $30
Fred: $75-$30 = $45