Question 530447: oe has a collection of nickels and dimes that is worth $7.65. If the number of dimes was doubled and the number of nickels was increased by 35, the value of the coins would be $14.30. How many nickels and dimes does he have?
Found 2 solutions by oberobic, MathTherapy:
Answer by oberobic(2304)   (Show Source):
You can put this solution on YOUR website! 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.
Answer by MathTherapy(10858)  (Show Source):
You can put this solution on YOUR website!
Joe has a collection of nickels and dimes that is worth $7.65. If the number of dimes was doubled and the number of nickels was increased by 35, the value of the coins would be $14.30. How many nickels and dimes does he have?
Let amount of dimes be D, and amount of nickels, N
Then: . 1(D) + .05(N) = 7.65 ------ 10D + 5N = 765 ----- Multiplying by 100 to clear decimals ----- eq (i)
Also, .1(2D) + .05(N + 35) = 14.3 ----- .2D + .05N + 1.75 = 14.3 ------- .2D + .05N = 12.55 ------- 20D + 5N = 1,255 ----- Multiplying by 100 to clear decimals ----- eq (ii)
10D + 5N = 765 ------- eq (i)
20D + 5N = 1,255 ----- eq (ii)
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- 10D = - 490 ----- Subtracting eq (ii) from (i)
D, or amount of dimes =  , or  , or 
10(49) + 5N = 765 ------- Substituting 49 for D in eq (i)
490 + 5N = 765
5N = 765 – 490
5N = 275
N, or amount of nickels =  , or 
I'll leave the check up to you to perform.
Send comments and “thank-yous” to “D” at MathMadEzy@aol.com
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