Question

Senor Pena found some change on the floor while cleaning a classroom. He found a total of 6 coins that consisted of quarters and nickels. If the total change was $1.30, how many of each coin did he find?

Answer 1

There are 5 quarters and 1 nickel

Explanation:

Let Q and N be the numbers of Quarters and Nickels that Senor Pena found, respectively.

The value of each coin is $0.25 for quarters and $0.05 for each nickel

The total of $1.30 would be the result of:

1) Quarters: $0.25*Q, and

2) Nickels: $0.05*N

So we can write: $0.25*Q + $0.05*N = $1.30

We also know he found 6 coins, so:

Q + N = 6

We have two equations and two unknowns. We can use substitution to find the answer.

Rearrange the second equation to isolate one of the two variables. lets isolate Q:

Q = 6-N

We can use this definition of Q in the first equation by substitution:

$0.25*Q + $0.05*N = $1.30

$0.25*(6-N) + $0.05*N = $1.30

Leaving off the $ signs for clarity:

0.25(6-N) + 0.05N = 1.30

1.5 - 0.25N + 0.05N = 1.30

-0.2N = -0.20

N = 1

There is 1 nickel

Since Q = 6-N, Q = 5

There are 5 quarters and 1 nickel

CHECK

Do 5 quarters and 1 nickel add to $1.30?

5*($0.25) + 1*($0.05) = $1.30?

$1.25 + $0.05 = $1.30 YES