Question 530447
With coin problems you have to keep track of the count of each coin and the value.
n = number of nickels
5n = value of the nickels in cents
d = number of dimes
10d = value of the times in cents
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5n + 10d = 765 cents
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2(10d) + 5(n+35) = 1430 cents
20d + 5n + 165 = 1430
20d + 5n = 1265
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With two equations and two unknowns, you can solve the system of equations.
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5n + 10d = 765
5n + 20d = 1265
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-10d = -500
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d = 50
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Substitute d = 50 to find n.
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5n + 10d = 765
5n + 10(50) = 765
5n = 265
n = 53
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Check the values to make sure the above solution is the correct answer.
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5(53) = 265
10(50) = 500
265 + 500 = 765 cents
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Check the other equation, too.
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2(10(50)) + 5(53+35) = 1430 ??
2(500) + 265 + 175 = 1430
Correct.
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Answer: Joe has 53 nickels and 50 dimes.
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Done.