SOLUTION: Hi, please help me solve the question: A man spends $4.00 to buy lemons. If the price of each lemon were 4 cents less, he could buy 50 more for the same amount of money. What w

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Hi, please help me solve the question: A man spends $4.00 to buy lemons. If the price of each lemon were 4 cents less, he could buy 50 more for the same amount of money. What w      Log On


   

Question 619580: Hi, please help me solve the question:
A man spends $4.00 to buy lemons. If the price of each lemon were 4 cents less, he could buy 50 more for the same amount of money. What was the price of each lemon?
Thank you!
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +p+ = the price of a lemon in cents
The number of lemons he bought was +400%2Fp+
+p+-+4+ is 4 cents less than the price of a lemon
+%28+p+-+4+%29%2A%28+400%2Fp+%2B+50+%29+=+400+
+400+%2B+50p+-+1600%2Fp+-+200+=+400+
+50p+-+1600%2Fp+-+200+=+0+
Multiply both sides by +p+
+50p%5E2+-+1600+-+200p+=+0+
+p%5E2+-+4p+-+32+=+0+
+%28+p+-+8+%29%2A%28+p+%2B+4+%29+=+0+
+p+=+8+
Each lemon cost 8 cents
check:
+%28+p+-+4+%29%2A%28+400%2Fp+%2B+50+%29+=+400+
+%28+8+-+4+%29%2A%28+400%2F8+%2B+50+%29+=+400+
+4%2A%28+50+%2B+50+%29+=+400+
+4%2A100+=+400+
+400+=+400+
OK