# A bicycle question

• Oct 12th 2009, 03:14 AM
ronaldj
A bicycle question
Peter agreed to work after school for 8 weeks at a fixed weekly rate. But instead of being given only money, he was to be given $85 and a bicycle. However, Peter worked only 5 weeks at the fixed weekly rate and was given$25 and the bicycle. How much was the bicycle worth?

-- I saw somewhere the answer is $75 but not sure how to get that. -- originally i took the$85 and divided by 8 weeks, and that gave me $10.62 -- then i took the 5 weeks and multiplied it by$10.62

-- that gave me 53.12

-- thought about minusing $25 from that... but am totally STUMPED. p.s. yes, I know I am bad @ math! Thanks for reading! • Oct 12th 2009, 04:12 AM earboth Quote: Originally Posted by ronaldj Peter agreed to work after school for 8 weeks at a fixed weekly rate. But instead of being given only money, he was to be given$85 and a bicycle. However, Peter worked only 5 weeks at the fixed weekly rate and was given $25 and the bicycle. How much was the bicycle worth? -- I saw somewhere the answer is$75 but not sure how to get that.

-- originally i took the $85 and divided by 8 weeks, and that gave me$10.62

-- then i took the 5 weeks and multiplied it by $10.62 -- that gave me 53.12 -- thought about minusing$25 from that... but am totally STUMPED.

p.s. yes, I know I am bad @ math!

Let w denote the money for work in 1 week and b the price of the bicycle.

Then you know (talking about money only!):

$\left|\begin{array}{rcl}8w-b&=&85\\5w-b&=&25 \end{array} \right.$

Solve this system of equations for w and b
Spoiler:
I've got w = $20 and b =$75
• Oct 12th 2009, 04:20 AM
ronaldj
Many thanks Earboth!
for your explanation and I LOVE the spoiler!! A nice way to do that part for the answer.

No wonder you are a Super Member!