How much is the bicycle worth?

[Marcelo Arevalo]

John agreed to work after school for 8 weeks for a fixed weekly rate. But instead of being given only money for his work, John agreed to receive \$850.00 and a bicycle. After 5 weeks, John got sick. He was given \$250.00 and a bicycle. How much is the bicycle worth?

 

[Marcelo Arevalo]

I was working on this solution :
8 weeks = 850 + bicycle
5 weeks = 250 + bicycle

Solving for weekly rate :
850 / 8 + bicycle/8 = 250/5 + bicycle/5
850 /8 - 250/5 = bicycle/8 - bicycle/5

now I am stucked... am I doing the right thing??
please help. thank you.

 

[Greg]

Let y be the value, in cash, for the 8 weeks worked and let b be the cost of the bicycle. We can then form two equations:

y = 850 + b

and

5y/8 = 250 + b.

Subtracting the two equations, we have

y - 5y/8 = 850 + b - (250 + b) = 600, 3y/8 = 600.

Solving for y, we find y = 1600. With the equation y = 850 + b, b = 1600 - 850 = 750, so the bicycle is worth \$750.00.

* A note on using \$ signs here: Use \$ for the text following dollar signs to display correctly.

 

[Marcelo Arevalo]

Wow! Thank you very much!

 

[phymat]

Hello, Marcelo Arevalo. If you are satisfied with any of the solutions given above (you seem to be), then I request you to use the thread tools to mark this thread as solved.