Final answer:
Kevin and Randy Muise have 47 quarters and 15 nickels in their jar which contains a total of 62 coins worth $12.50, solved using a system of linear equations.
Step-by-step explanation:
The student asked about how many quarters and nickels Kevin and Randy Muise would have if they own a jar with 62 coins totaling a value of $12.50. To solve this problem, we set up a system of equations using two variables: Let x be the number of quarters and y be the number of nickels. We have two equations:
The first equation represents the total number of coins: x + y = 62.
The second equation represents the total value of coins in dollars: 0.25x + 0.05y = 12.50.
By solving this system of equations, we can determine the number of quarters and nickels.
Step-by-Step Solution:
Multiply the second equation by 20 to eliminate decimals: 5x + y = 250.
Subtract the first equation from the new version of the second equation to solve for x: (5x + y) - (x + y) = 250 - 62, which simplifies to 4x = 188. Dividing both sides by 4, we find x = 47, indicating that there are 47 quarters.
Substitute x = 47 into the first equation to find y: 47 + y = 62, which simplifies to y = 15, indicating there are 15 nickels.
Therefore, the jar contains 47 quarters and 15 nickels.