College Algebra Word Application Problem

Question

We have a jar of coins, all quarters and pennies. All together, we have 276 coins, and the total value of all coins in the jar is $ 31.56. How many quarters are there in the jar?

quarters=

Answer 1

This problem can be solved with a simple system of equations.

First, we assign each of the coins a variable: The number of quarters = Q and the number of pennies = P. Then we translate each of the descriptions about them into mathematical equations using our variables.

"All together, we have 276 coins" just means Q + P = 276, and "the total value of all coins in the jar is $31.56" becomes 25Q + 1P = 3156 (each of the coins' values times the number of each coin--we can drop the one next to the P, but I left it for clarity. Also, everything is in cents now so the dollar sign and decimal can go away). Since we're trying to find the number of quarters, let's substitute P from the first equation (rearranged as P = 276 - Q) into the second, which becomes: 25Q + (276 - Q) = 3156

Solve (preserving the order of operations), and Q = 120. Success!