Set up Let the dimes = d Let the pennies = p Let the quarters = q
Equations You cannot mean that the pennies and dimes have equal numbers. That would mean that each had 21.5 members. Now could you mean that the dime and penny amount could be the same with 43 coins that total 4.00. Four dollars means that you need 40 dimes alone. It must mean that you are including quarters.
p + d + p = 43 (1) p = d (2) p +10d +25q = 451 (3)
Note how this last equation = was derived. You have to multiply the dimes by 10 and he quarters by 100 and the total by 100 to get the numbers all in pennies.
Put the results of 2 into 1. 2p + q = 43 (4) You need to modify equation 3 as well. p + 10p + 25q = 451 11p + 25q = 451 (5)
Solve the new equations 2p + q = 43 (4) 11p + 25q = 451 (5)
Multiply 4 by 25 25(2p- + q = 43) 50p + 25q = 1075 (6) Subtract (5) from (6) 11p + 25q = 451 39p = 624 Divide by 39 p = 624 / 39 p = 16
Since the pennies and dimes are equal there are 16 dimes p + d + q = 43 16 + 16 + q = 43 32 + q = 43 q = 11
