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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