How many Quarters? How many Pennies? How many dimes? Solve by using systems of equations by substitution

Question

You have 20 coins total. These are quarters dimes and pennies. There are 5 times as many pennies as dimes. The 20 coins are worth $2.30 total. How many Quarters? How many Pennies? How many dimes? Solve by using systems of equations by substitution

Answer 1

Q, D, P = numbers of quarters, dimes and pennies. Q+D+P=20. P=5D, so Q+D+5D=20 and Q+6D=20.

Value=25Q+10D+P=230 pennies, so 25Q+10D+5D=230, 25Q+15D=230, so 25Q=230-15D, 5Q=46-3D.

Q=20-6D, so 5Q=100-30D=46-3D. 54=27D, D=2, P=5*2=10 and Q=20-6*2=8.

CHECK: Q+D+P=8+2+10=20. VALUE=8*0.25+2*0.10+0.10=$2.30.

Solution: 8 quarters, 2 dimes, 10 pennies.