Question

Kevin and randy muise have a jar of 44 coins all of which are either quarters or nickels the total value of the coins in the jar is $6.40

Answer 1

21 quarters and 23 nickels. The quarters value at $5.25 and the nickels value at $1.15.

Explanation:

This situation has two unknowns - the total number of nickels and the total number of quarters. Because we have two unknowns, we will write a system of equations with two equations using the two unknowns.

• 
  `n+q=44` is an equation representing the total number of coins
• 
  `0.05n+0.25q=6.40` is an equation representing the total value in money based on the number of coin. 0.05 and 0.25 come from the value of a nickel and quarter individually.

We write the first equation in terms of q by subtracting it across the equal sign to get
`n=44-q`. We now substitute this for n in the second equation.

`0.05(44-q)+0.25q=6.40\\2.2-0.05q+0.25q=6.40\\2.2+0.20q=6.40`

After simplifying, we subtract 2.2 across and divide by the coefficient of q.

`2.2+0.20q=6.40\\0.20q=4.20\\q=21`

We now know of the 44 coins that 21 are quarters. To find the total value of the quarters, we multiply 21 by 0.25 and find 5.25.

Since there are 21 quarters out of 44, there must be 23 nickels. To find the total value of the nickels, we multiply 23 by 0.05 and find 1.15.