Kevin and Randy muise have a jar containing 55 coins, all of which are either quarters or nickels. The total value of the coins in the jar is $9.35 how many of each type of coin do they have?

The number of quarters in the jar = 33

The number of nickels = 22

Step-by-step explanation:

Let us assume the total number of quarters in the jar = m

Now, as the total number of coins in the jar = 55

SO, the number of nickels in the jar = 55 - m

Also, 1 quarter = $0.25

So, m quarters = m x ($0.52) = $ 0.25 m ... (1)

1 nickel = $0.05

So, (55 - m) nickels = (55 - m) x ($0.05) = $ (2.75 - 0.05 m) ... (2)

Total Value in the jar = $9.35

⇒ The value of m quarters + (55 - m) nickels = $9.35

or, $ 0.25 m + $ (2.75 - 0.05 m) = $9.35 ... from (1 and 2)

or, 0.25 m + 2.75 - 0.05 m = 9.35

⇒ 0.2 m = 6.6

or, m = 6.6/0.2 = 33

or, m = 33

Hence the number of quarters in the jar = m = 33

The number of nickels = 55 - m = 55 - 33 = 22