Question

Ari has a total of 22 coins consisting of pennies and nickels. The total value of coins is $0.54. how many pennies does he have?

Answer 1

There are 8 nickels and 14 pennies

Explanation:

Represent the number of pennies by p and nickels by n. Then:

p + n = 22, or n = 22 - p

Coin values:

($0.01/penny); ($0.05/nickel). Therefore, the relation showing the amounts of money involved is:

($0.01/penny)p + ($0.05/nickel)n = $0.54.

But we found earlier that n = 22 - p. Therefore, the previous equation becomes:

($0.01/penny)p + ($0.05/nickel)(22 - p) = $0.54.

Multiply all three terms by 100 to eliminate the decimal fractions:

1p + 5(22 - p) = 54, or:

1p + 110 - 5p = 54, or:

-4p = -56

Thus, p = 14. If p = 14, then n = 22 - 14 = 8.

There are 8 nickels and 14 pennies.

Check: 8($0.05) + 14($0.01) = $0.54 (correct)