Shawna found coins worth $4.32. One-fourth of the found coins are pennies and one-sixth are quarters. The number of nickels found is 1.5 times the number of quarters. How many of each coin did Shawna find?

8 quarters

12 nickels

12 pennies

16 dimes

Step-by-step explanation:

Let the number of coins = x

One-fourth of the found coins are pennies ⇒ 0.25 x

one-sixth are quarters ⇒ (1/6) x

The number of nickels found is 1.5 times the number of quarters⇒ 1.5 * (1/6) x

Let ⇒ There no dimes.

Penny = 1 cent, quarter = 25 cents, nickel = 5 cents

$4.32 = 432 cents

So,

0.25x + (1/6) x * 25 + 1.5 * (1/6) x * 5 = 432

Solve for x

(17/3) x = 432

x = 432*3/17 = 76.24

The number of coins must be integer number so, we should assume there are some of coins are dimes

Let the number of coins that is dimes = y

The number of total coins = x

So, 0.25 x + (1/6) x + 1.5 * (1/6) x + y = x

∴ y = x - (0.25 x + (1/6) x + 1.5 * (1/6) x) = (1/3) x ⇒ (1)

And the total coins worth $4.32 = 432 cents

0.25x + (1/6) x * 25 + 1.5 * (1/6) x * 5 + 10 y = 432

By substitution with y from (1)

∴ 0.25x + (1/6) x * 25 + 1.5 * (1/6) x * 5 + 10 * (1/3) x = 432

Solve for x, combine the terms contain x

∴ (0.25 + (1/6) * 25 + 1.5 * (1/6) * 5 + 10 * (1/3)) x = 432

∴ 9 x = 432

∴ x = 432/9 = 48 coins

So, The number of quarters = 1/6 x = 8 quarters

The number of nickels = 1.5 number of quarters = 1.5*4 = 12 nickels

The number of pennies = 1/4 x = 12 pennies

The number of dimes = 1/3 x = 16 dimes