Write and solve an equation to find the number of each type of coin.

Question

A person has quarters, dimes, and nickels with a total value of 500 cents. The number of nickles is twice the number of quarters. The number of dimes is four less than the number of quarters. Write and solve an equation to find the number of each type of coin.

Answer 1

Let's say that x is the number of quarters. Quarters are worth 25 cents, nickels are worth 5 cents, and dimes are worth 10 cents. There are 2 times as many nickels as quarters, so 2x. There are 4 less dimes than quarters, so x-4. Multiply each with their amount in cents, and added together they must equal 500.

25x+5(2x)+10(x-4)=500

25x+10x+10x-40=500

45x-40=500

45x=540

x=12

So 12 quarters, (2x12=24) 24 nickels, and (12-4=8) 8 dimes

Answer 2

Q = No. of quarters = Value 25Q cents

N = number of nickels , Value = 5N cents

D = No. of dimes Value = 10D cents

Given N =  2 Q

D = Q -4

500 = 25 Q + 5 N + 10 D = 25Q + 5 (2Q) + 10 ( Q-4) = 25 Q + 10 Q + 10 Q - 40 = 45 Q - 40

Given Q = 540/45 = 12

N= 24

D= 12- 4 =8