Question

You have 64 coins, consisting of pennies, nickels, and quarters. The value of

the coins is $4.60. You also know that you have three times as many nickels as
quarters. Find the quantity of each type of coin.

Answer 1

There are 20 pennies, 33 nickels and 11 quarts.

Explanation:

We are given the following information in the question:

1 penny = 1 cent

1 nickel = 5 pennies = 5 cent

1 quarter = 25 pennies = 25 cents

Let x be the number of pennies, y be the number of nickels and z be the number of quarts.

Total number of coins = 64

Amount of money = $4.60 = 460 cents

The, we have the following equations:

`x +y +z =64\\x + 5y + 25z = 460`

Also, we have three times as many nickels as quarters.

`y = 3z`

Putting this value in the above equation:

`x + 4z =64\\x + 40z = 460`

Solving the two equation, we have

x = 20, z = 11

`y = 3z = 33`

Hence, there are 20 pennies, 33 nickels and 11 quarts.

Answer 2

There are 20 pennies, 33 nickels and 11 quarters

Explanation:

- You have 64 coins, consisting of pennies, nickels, and quarters

- The value of the coins is $4.60

- Assume that there are p pennies, n nickles, and q quarters

∴ p + n + q = 64 ⇒ (1)

- Lets find the value of each types of coins

∵ 1 penny = 1 cent ⇒ p = p cents

∵ 1 nickel = 5 cents ⇒ n = 5n cents

∵ 1 quarter = 25 cents ⇒ q = 25q cents

∵ 1 dollar = 100 cents ⇒ $4.60 = 4.60 × 100 = 460 cents

∴ p + 5n + 25q = 460 ⇒ (2)

- You also know that you have three times as many nickels as quarters

∴ n = 3q ⇒ (3) ⇒ the number of nickles by quarters

∵ 5n = 5(3q)

∴ 5n = 15q ⇒ (4) ⇒ the values of nickles by quarters

- Substitute (3) in equation (1) and (4) in equation (2)

∴ p + 3q + q = 64

∴ p + 4q = 64 ⇒ (5)

∴ p + 15q + 25q = 460

∴ p + 40q = 460 ⇒ (6)

- Subtract equation (5) from equation(6) to eliminate p

∴ 36q = 396

- Divide both sides by 36

∴ q = 11

- Substitute the value of q in equation (5)

∴ p + 4(11) = 64

∴ p + 44 = 64

- Subtract 44 from both sides

∴ p = 20

- Substitute the value of q in (3)

∴ n = 3(11) = 33

∴ n = 33

There are 20 pennies, 33 nickels and 11 quarters