SOLUTION: Annie has a piggy bank consisting of quarters dimes and nickels. She has a total 74 coins in the bank totaling 11.35$. There are half as many dimes as quarters. How many nickels do
Question 1204793: Annie has a piggy bank consisting of quarters dimes and nickels. She has a total 74 coins in the bank totaling 11.35$. There are half as many dimes as quarters. How many nickels does Annie have? Found 2 solutions by josgarithmetic, math_tutor2020:Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
COIN HOWMANY VALUE
Quarter 2d 0.25*2d
Dime d 0.1*d
Nickel 74-d-2d 0.05(74-3d)
TOTAL 74 11.35
Let x = number of dimes
2x = number of quarters
x+2x = 3x = number of dimes and quarters
Annie has 74 coins total.
3x of them are either quarters or dimes, so the remaining 74-3x coins must be nickels.
x = number of dimes
10x = value of the dimes in cents
2x = number of quarters
25*2x = 50x = value of the quarters in cents
74-3x = number of nickels
5*(74-3x) = 370 - 15x = value of the nickels in cents
total value in cents = 10x+50x+370-15x = 45x+370
Set this equal to the total amount Annie has which is 1135 cents (aka $11.35)
45x+370 = 1135
45x = 1135-370
45x = 765
x = 765/45
x = 17
So,
number of dimes = x = 17
number of quarters = 2x = 2*17 = 34
number of nickels = 74-3x = 74-3*17 = 23
In short,
number of dimes = 17
number of quarters = 34
number of nickels = 23
Check
17 dimes + 34 quarters + 23 nickels = 17*10 + 34*25 + 23*5 = 1135 cents = $11.35
This helps confirm the answer.
Further confirmation comes from the fact that 17+34+23 = 74