SOLUTION: I have a word problem and would really appreciate your help. Nana found some coins under her sofa pillows. There were equal numbers of nickels and quarters, and twice as many

Question 156234This question is from textbook
: I have a word problem and would really appreciate your help.
Nana found some coins under her sofa pillows. There were equal numbers of nickels and quarters, and twice as many half-dollars as quarters. If she found $2.60 in all, how many of each denomination of coin did she find? This question is from textbook

Answer by kdr(11) (Show Source): You can put this solution on YOUR website!
Let x equal the number of nickels and the number of quarters.
Let y equal the number of half-dollars.
Since there are twice as many half-dollars as quarters:
y=2x
Value of nickels would be .05 times x, value of quarters would be .25 times x, and value of half-dollars would be .5 times y, giving us this equation:
.05x + .25x + .5y = 2.60
Substitute 2x for y:
.05x + .25x + .5(2x) = 2.60
Simplifying .5 times 2 is 1, so:
.05x + .25x + x = 2.60
Combine like terms:
1.3x = 2.60
Multiple both sides by 10:
13x = 26
Divide both sides by 13:
x = 2
y = 4
So, there are 2 nickels, 2 quarters, and 4 half-dollars.
Checking the solution:
2 nickels = .10
2 quarters = .50
4 half-dollars = 2.00
Total value = 2.60
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