Kevin and Randy Muise have a jar containing 71 ​coins, all of which are either quarters or nickels. The total value of the coins in the jar is ​$11.95. How many of each type of coin do they​ have?

Answer 1

Let's let q represent the NUMBER of quarters and n represent the NUMBER of nickers. Since there are a total of 71 coins , we can write:

q + n = 71

Then since each quarter is worth twenty-five cents or 0.25 and each nickel is worth five cents or 0.05, we can write:

0.25q + 0.05n = 11.95

To solve these two equations with two unknowns, use substitution.

From the first equation we can write that n= 71 -q

Substitute this expression for n into the second equation:

0.25q + 0.05(71 - q) = 11.95

Solve for q using inverses operations, combining like terms, and the distributive property:

0.25q + 3.55 - 0.05q = 11.95

0.20q + 3.55 = 11.95

0.20q + 3.55 - 3.55 = 11.95 - 3.55

0.20q = 8.40

0.20q /0.20 = 8.40/0.20

q= 42

So the number is quarters is 42 . The number of nickels will be 71 - 42 or 29 nickels.

To check, 42 quarters would be worth $10.50 (0.25 * 42)

29 nickels would be worth $1.45 (0.05 * 29)

$10.50 + 1.45 = $11.95