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

8 quarters

12 nickels

12 pennies

16 dimes

Step-by-step explanation:

The trick is to ASSUME the dimes.

Start by thinking about the three explicit premises and the one implicit premise.

1) Quarters = 1/6 of total coins

2) Nickels = 1.5 the number of quarters

3) Pennies = 1/4 of total coins

Also, ASSUME an unknown number of dimes to fill in the gap.

48 Total Coins = $4.32

⅙ of 48 = 88 quarters = $2.00

1.5 x 8 = 1212 nickels = $0.60

¼ of 48 = 1212 pennies = $0.12

Add those coins = $2.72

Take the known total and minus this sum.

$4.32 - $2.72 = $1.60

16 dimes = $1.60

Thus, you have the following:

8 quarters (⅙ of total coins)  $2.00

12 nickels (1.5 the number of quarters)$0.60

12 pennies (¼ the number of total coins)$0.12    

+16 dimes    $1.60

Total Coins48      $4.32