SOLUTION: Six grapefruits cost as much as ten oranges. The cost of a dozen grapefruit and two dozen oranges is 33$. How many cents does one orange cost?

Algebra ->  Customizable Word Problem Solvers  -> Finance -> SOLUTION: Six grapefruits cost as much as ten oranges. The cost of a dozen grapefruit and two dozen oranges is 33$. How many cents does one orange cost?      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 738958: Six grapefruits cost as much as ten oranges. The cost of a dozen grapefruit and two dozen oranges is 33$. How many cents does one orange cost?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
What we really want to know, or find, are the prices for oranges grapefruits.
n = dollars per orange
g = dollars per grapefruit
We know that "dozen" means 12.

Analyze the description:

Six grapefruits cost as much as ten oranges.
6%2Ag=10%2An

The cost of a dozen grapefruit and two dozen oranges is 33$.
12%2Ag%2B24%2An=33

The system is the set of those two equations,
6%2Ag=10%2An AND 12%2Ag%2B24%2An=33.
Solve the system for g and n. Remember, these are in dollars per fruit, and you were asked for CENTS per ORANGE. You are REALLY looking for n.

METHOD:
What you could do is solve one of the equations for g, substitute this into the other equation, and then solve for n. Compute and simplify; and you will have your answer.