Let P = number of coins of pennies (1 penny = 1 cent) Let N = number of coins of nickels (1 nickel = 5 cents) Let D = number of coins of dimes (1 dime = 10 cents) Let Q = number of coins of quarters (1 quarter = 25 cents)
a) P + N + D + Q = 284 coins, but P = 173 coins, then: 173 + N + D + Q =284 coins (1) N + D + Q = 111 coins
b) D = N + 5 OR D - N =5 coins (2) D - N = 5 coins
c) Let's find the VALUE in CENTS of (1) that is N + D + Q = 111 coins 5N + 10D + 25 Q = 2,278 - 173 (1 PENNY) (3) 5N + 10D + 25Q = 2105 cents Now we have 3 equation with 3 variables:
(1) N + D + Q = 111 coins (2) D - N = 5 coins (3) 5N + 10D + 25Q = 2105 cents Solving it gives: 17 coins N ( x 5 = 85 cents) 22 coins D ( x 10 = 220 cents) 72 coins D ( x 25 = 1,800 cents) and 173 P, proof: that makes a total of 85+2201800+172 =2,278 c or $22.78
