SOLUTION: kevin and randy muise have a jar containing 31 coins, all of which are either quarters or nickels. The total value of the coins in the jar is $5.35. How many of each type of coin d
Question 1034527: kevin and randy muise have a jar containing 31 coins, all of which are either quarters or nickels. The total value of the coins in the jar is $5.35. How many of each type of coin do they have? Answer by ikleyn(52788) (Show Source):
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kevin and randy muise have a jar containing 31 coins, all of which are either quarters or nickels.
The total value of the coins in the jar is $5.35. How many of each type of coin do they have?
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Coin problems are straight forward to solve. You write two equations - one for the total number of coins and the other for the total value of the coins.
Let n = the number of nickles
Let q = the number of quarters
Then for your problem we have
(1) n + q = 31 and
(2) 5*n + 25*q = 100*5.35 (always work in cents to avoid decimal numbers) or
(3) 5*n + 25*q = 535
Now substitute n of (1) into (3) and get
(4) 5*(31 - q) + 25*q = 535 or
(5) 155 - 5*q + 25*q = 535 or
(6) 20*q = 535 - 155 or
(7) 20*q = 380 or
(8) q = 19
Then using (1) we get
(9) n + 19 = 31 or
(10) n = 12
Let's check these values.
.05*12 + .25*19 = 5.35. Yes!
Answer: Kevin and Randy have 12 nickles and 19 quarters in the jar.
