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Question 229377: The sum of three numbers is 16. The sum of twice the first number, 3 times the second number, and 4 times the third number is 46. The difference between 5 times the first number and the second number is 31. Find the three numbers.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Three numbers, x, y, z
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Write an equation for each statement:
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"The sum of three numbers is 16."
x + y + z = 16
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" The sum of twice the first number, 3 times the second number, and 4 times the third number is 46."
2x = 3y + 4z = 46
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" The difference between 5 times the first number and the second number is 31."
5x - y = 31
-y = 31 - 5x
y = 5x - 31; multiplied by -1
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Find the three numbers.
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Replace y with (5x-31) in the 1st and 2nd equation
x + (5x-31) + z = 16
6x + z = 16 + 31
6x + z = 47
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2x = 3(5x-31) + 4z = 46
2x = 15x - 93 + 4z = 46
17x + 4z = 46 + 93
17x + 4z = 139
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Multiply the 1st 2 unknown equation by 4, subtract the 2nd
24x + 4z = 188
17x + 4z = 139
----------------subtraction eliminates z
7x = 49
x = 
x = 7
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Find z using 6x + z = 47
6(7) + z = 47
42 + z = 47
z = 47 - 42
z = 5
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Use y = 5x - 31 to find y
y = 5(7) - 31
y = 35 - 31
y = 4
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Check our solution in the statement:
"The sum of twice the first number, 3 times the second number, and 4 times the third number is 46."
2(7) + 3(4) + 4(5) =
14 + 12 + 20 = 46
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