Modeling with Systems

Question

Kevin and Randy Muise have a jar containing

49

​coins, all of which are either quarters or nickels. The total value of the coins in the jar is

​$ 7.65.

How many of each type of coin do they​ have?

Answer 1

Let's define variables to represent the number of each type of coin:

1. Let q be the number of quarters
2. Let n be the number of nickels

Step 1: Set Up the Equations

1. The total number of coins is 49, so:q+n=49q+n=49
2. The total value of the coins is $7.65, which is 765 cents, and knowing that quarters are worth 25 cents and nickels are worth 5 cents, we can write:25q+5n=76525q+5n=765

Step 2: Solve for One Variable

From the first equation, solve for n:

n=49−qn=49−q

Substituting this into the second equation:

25q+5(49−q)=76525q+5(49−q)=765

Step 3: Distribute and Solve for q

25q+245−5q=76525q+245−5q=76520q+245=76520q+245=76520q=52020q=520q=26q=26

Step 4: Solve for n

n=49−26n=49−26n=23n=23

Step 5: Final Answer

Kevin and Randy Muise have 26 quarters and 23 nickels.