Kevin and Randy Muise have a jar containing 58 coins , all of which are either quarters or nickles. The total value of the coins in the jar is $10.90. How many of each type of coin do they have?

Question

Kevin and Randy Muise have a jar containing 58 coins , all of which are either quarters or nickles. The total value of the coins in the jar is $10.90. How many of each type of coin do they have?

Answer 1

Hi Selah B

18 nickels

40 quarters

Given total number of coins, 58 and total value of coins $10.90, you can use a system of equations and substitution to solve your problem

Let n = nickels

Let q = quarters

We can set up an Equation for the total number of coins

n + q = 58

q = 58 - n

We can set up an Equation for total value

0.05n + 0.25q = 10.90

We can use our substitution from above to get everything in terms of n and solve for n

0.05n + .25(58 - n) = 10.90

0.05 n + 14.50 - 0.25n = 10.90

Combine like terms

-0.20n + 14.50 = 10.90

Subtracting 14.50 from both sides of the equation

-0.20n = -3.60

Divide both sides by -0.20

n = 18 so we have 18 nickels

q = 58 - n = 58 - 18 = 40 we have 40 quarters

Checking

0.05(18) + 0.25(40) = 10.90

0.90 + 10.00 = 10.90.

There are other ways to do the problem but I hope you find this useful.