Answer:
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
