Question 935847
x = number of dimes
y = number of quarters
z = number of half-dollars
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x + y + z = 70
10x + 25y + 50z = 1775
y = 3x
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put the system of linear equations into standard form
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x + y + z = 70
10x + 25y + 50z = 1775
3x - y = 0
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solution:
x = number of dimes = 15
y = number of quarters = 45
z = number of half-dollars = 10
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now by elimination:
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x + y + z = 70
3x - y = 0
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add the above two equations:
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4x + z = 70
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10x + 25y + 50z = 1775
25(3x - y = 0)
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add the above two equations:
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85x + 50z = 1775
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-50(4x + z = 70)
85x + 50z = 1775
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add the above two equations:
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-115x = 1775 - 3500
x = (1775 - 3500)/-115
x = 15
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3x - y = 0
y = 3*15
y = 45
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4x + z = 70
4*15 + z = 70
z = 10
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solution by elimination:
x = number of dimes = 15
y = number of quarters = 45
z = number of half-dollars = 10
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