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

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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) About Me  (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

Do you see what to do with this?

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0.5d%2B0.1d%2B0.05%2874-3d%29=11.35
0.6d%2B0.05%2A74-0.15d=11.35
0.45d=11.35-0.05%2A74
d=%2811.35-0.05%2A74%29%2F0.45
highlight%28d=17%29----------dimes

The question was how many nickels.
74-3%2A17
74-51
highlight%28highlight%2823%29%29---------nickels

Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

"There are half as many dimes as quarters" which flips around to "There are twice as many quarters as dimes".

# of quarters = 2*(# of dimes)

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


Answer: She has 23 nickels