Question 1002802: A piggy bank contains nickels, dimes, and quarters. If there are a total of fourteen coins, the value of the nickels is equal to the value of the dimes, and the entire set is worth a total of $1.30, how many nickels are there?
Found 2 solutions by josmiceli, addingup:
Answer by josmiceli(19441)   (Show Source):
Answer by addingup(3677)  (Show Source):
You can put this solution on YOUR website! There are 14 coins in nickels, dimes, quarters:
n+d+q= 14 (equation 1)
Nickels, dimes and quarters add up to 1.30:
0.05n+0.10d+0.25q= 1.30 (equation 2)
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The value of the nickels = value of dimes:
0.05n= 0.10d
And, since there are two nickels in every dime, in order to have the same number of coins you would need twice as many dimes(count coins, not money)
n= 2d
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2d+d+q= 14 Add d on left:
3d+q= 14 Subtract 3d on both sides:
q= -3d+14
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Going back to equation 2:
0.05n+0.10d+0.25q= 1.30 We just said n= 2d, substitute:
0.05(2d)+0.10d+0.25q= 1.30 We also just said q= -3d+14, substitute:
0.05(2d)+0.10d+0.25(-3d+14)= 1.30 Multiply to get rid of parenthesis:
0.10d+0.10d-0.75d+3.50= 1.30 Add d on left and subtract 3.50 on both sides:
-0.55d=-2.20 Divide both sides by -0.55 (and remember, -/-= +)
d= 4 You have 4 dimes. And the nickels are twice as many:
n= 4*2= 8 And the quarters are -3d+14:
q= -3d+14 and we have 4 dimes, so:
q= -3(4)+14
q= -12+14= 2 we have 2 quarters.
Proof:
4 dimes: 0.40
8 nickels: 0.40
2quarters: 0.50
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Total:.......1.30 We have the correct answer
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