How many of each denomination of coins does he​ have?

Question

A man has a box of coins that he uses when playing poker with friends. The box currently contains 35 coins, consisting of​ pennies, dimes, and quarters. The number of pennies is equal to the number of​ dimes, and the total value is ​$2.51. How many of each denomination of coins does he​ have?

Answer 1

P+D+Q = 35 = total number of coins

P=D number of pennies = number of dimes

P+10D +25Q = 251 = total value of the coines

D+10D +25Q = 251

11D +25Q = 251

22D +50Q =502 is equation I

D+D +Q = 35

2D +Q = 35

22D +11Q = 385 is equation II

subtract equation II from equation I

39Q = 502-385 = 117

Q = 117/39 = 3 quarters

2D +3 =35

2D = 32

D= 16 dimes

P=D = 16 pennies

16 + 10(16) + 25(3) = 176 + 75 = $2.51

3 quarters, 16 dimes and 16 pennies