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Kevin and Randy Muise have a jar containing 80 ​coins, all of which are either quarters or nickels. The total value of the coins in the jar is ​$11.80. How many of each type of coin do they​ have?

Respuesta :

mhanifa

Answer:

  • 39 quarters and 41 nickels

Step-by-step explanation:

Let the number of quarters be x and nickels be y.

Given:

  • Quarter is 25 cents
  • Nickel is 5 cents
  • Number of coins is 80
  • Total amount is $11.80 = 1180 cents

We have equations:

  • x + y = 80
  • 25x + 5y = 1180

Solve the system by elimination, subtract 5 times the first equation from the second one:

  • 25x + 5y - 5x - 5y = 1180 - 80*5
  • 20x = 780
  • x = 780/20
  • x = 39

Find the value of y:

  • 39 + y = 80
  • y = 80 - 39y = 41

Verify:

  • 25*39 + 5*41 = 975 + 205 = 1180

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