Question 1204793
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"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 = <font color=red>23</font>


In short,
number of dimes = 17
number of quarters = 34
number of nickels = <font color=red>23</font>


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 <font color=red size=4>23 nickels</font>
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