SOLUTION: susan, alonzo, and joe have a total of $70 dollars in their wallet. Alonzo has $6 less than susan. Joe has 2 times what Alonzo has. How much do they have in their wallet?

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Question 1151216: susan, alonzo, and joe have a total of $70 dollars in their wallet. Alonzo has $6 less than susan. Joe has 2 times what Alonzo has. How much do they have in their wallet?
Found 2 solutions by MathLover1, greenestamps:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
let the amount of dollars that Susan have be x, Alonzo y, and Joe z
if Susan, Alonzo, and Joe have a total of $70 dollars in their wallet, than
x%2By%2Bz=70........eq.1
if Alonzo has $6 less than Susan, than
y=x-6.......eq.2
Joe has 2 times what Alonzo has, we have
z=2y...........substitute y from eq.2
z=2%28x-6%29.......eq.3
go back to
x%2By%2Bz=70........eq.1 substitute y from eq.2 and z from eq.3
x%2B%28x-6%29%2B2%28x-6%29=70..........solve for x
x%2Bx-6%2B2x-12=70
4x-18=70
4x=70%2B18
4x=88
x=22

go to
y=x-6.......eq.2, substitute x
y=22-6
y=16

go to
z=2%28x-6%29.......eq.3, substitute x
z=2%2822-6%29
z=2%2816%29
z=32
so,
Susan has 22 dollars in her wallet
Alonzo has 16 dollars in his wallet
Joe has 32 dollars in his wallet


Answer by greenestamps(13209) About Me  (Show Source):
You can put this solution on YOUR website!


A solution using three variables is of course valid; but it requires a lot more work than is necessary.

Read the given information carefully so that the problem can be set up using a single variable:

let x = amount Susan has
then x-6 = amount Alonzo has ($6 less than Susan)
and then 2(x-6) = amount Joe has (twice what Alonzo has)

Now the equation for the total amount that the three of them has is in a single variable.

%28x%29%2B%28x-6%29%2B2%28x-6%29+=+70
x%2Bx-6%2B2x-12+=+70
4x-18+=+70
4x+=+88
x+=+22

ANSWER:
Susan: x = $22
Alonzo: x-6 = $16
Joe: 2(x-6) = $32

CHECK: total = $22+$16+$32 = $70