Question

Denny has a collection of coins. One fourth of his coins are pennies. One sixth of them are quarters. The number of nickels is 1.5 times the number of quarters. The rest of the coins are dimes. The total value of the coins is $4.32. How many of each coin does Denny have?

a) Pennies: 12, Quarters: 6, Nickels: 9, Dimes: 12

b) Pennies: 8, Quarters: 4, Nickels: 6, Dimes: 8

c) Pennies: 16, Quarters: 8, Nickels: 12, Dimes: 16

d) Pennies: 6, Quarters: 3, Nickels: 4.5, Dimes: 6

Answer 1

To solve the problem, we can use a system of equations to find the number of each coin. By assigning variables to represent the number of pennies, quarters, nickels, and dimes, we can set up and solve a system of equations to find the values of the variables. The solution is x = 12, y = 6, z = 9, and w = 12.

Step-by-step explanation:

To solve this problem, we can use a system of equations. Let's assign variables to represent the number of each coin. Let x be the number of pennies, y be the number of quarters, z be the number of nickels, and w be the number of dimes.

We can set up the following equations:

x = (1/4)(x + y + z + w)

y = (1/6)(x + y + z + w)

z = 1.5y

x + y + z + w = 432 (since the total value is $4.32)

Solving this system of equations, we find that x = 12, y = 6, z = 9, and w = 12. Therefore, Denny has 12 pennies, 6 quarters, 9 nickels, and 12 dimes.