SOLUTION: Marvin sold his bike for $20 more than one-third of what he paid for it. He sold it for $70. How much did he pay for it?

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Question 1023790: Marvin sold his bike for $20 more than one-third of what he paid for it. He sold it for $70. How much did he pay for it?
Found 2 solutions by Fombitz, lwsshak3:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Use a substitution,
X=a-b
Y=a%2Bb
So then,
%28a-b%29%2F%28a%2Bb%29-%28a%2Bb%29%2F%28a-b%29=X%2FY-Y%2FX
You want a common denominator XY

%28a-b%29%2F%28a%2Bb%29-%28a%2Bb%29%2F%28a-b%29=X%5E2%2F%28XY%29-Y%5E2%2F%28XY%29
%28a-b%29%2F%28a%2Bb%29-%28a%2Bb%29%2F%28a-b%29=%28X%5E2-Y%5E2%29%2F%28XY%29
So,
X%5E2=%28a-b%29%5E2=a%5E2-2ab%2Bb%5E2
Y%5E2=%28a%2Bb%29%5E2=a%5E2%2B2ab%2Bb%5E2
X%5E2-Y%5E2=a%5E2-2ab%2Bb%5E2-a%5E2-2ab-b%5E2
X%5E2-Y%5E2=-4ab
and
XY=%28a-b%29%28a%2Bb%29=a%5E2-b%5E2
Substituting,
%28a-b%29%2F%28a%2Bb%29-%28a%2Bb%29%2F%28a-b%29=%28-4ab%29%2F%28a%5E2-b%5E2%29

Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Marvin sold his bike for $20 more than one-third of what he paid for it. He sold it for $70. How much did he pay for it?
let x=amt Marvin paid for bike
20%2Bx%2F3=70
60+x=210
x=210-60=150
amt Marvin paid for bike=$150