Aman has a box of coins that he uses when he plays porker with his friends. the box contains 32 coins consisting of pennies, dimes, and quarters. the number of pennies is equal to the number of dimes and the total value is $3.71. how many denominations of coin does he have?

A bit tricky:. Transform P, D and Q in $

P+D+Q =32

0.01 P + 0.1 D + 0.25 Q = $3.71

But we know that te number of P is equal to the number of D, then we can write:

0.01 P + 0.1 P + 0.25 Q = $3.71  OR 0.11 P + 0.25 Q =$3.71

So we have 2 equations with 2 variables P and Q

P + P + Q =32 ( # P = # D) OR
2P + Q = 32
0.11 P +0.25 Q = 3.71
Solve the equation & you will find:

Number of Pennies = 11 (Total value $0.11)
Number of Dimes   =  11 (Total Value $1.1)
Number of Quarters = 10 (Total value $2.5)
     

Total                           = 32 (Total value $ 3.71)