Question 515466
x + y + z = 29
.
Twice the first number is 18 more than 3 times the second number.
2x = 3y +18
so
2x - 3y = 18
.
The third number minus the second number is 1 more than the first number.
z - y = x+1
so
-x -y +z = 1
.
x + y + z = 29
2x -3y = 18
-x -y +z = 1
.
Add the first and third equation
.
x + y + z = 29
-x -y +z = 1
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2z = 30
z = 15
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substitute z=15
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x +y + z = 29
x + y = 14
.
Recall
2x = 3y + 18
2x -3y = 18
and
x + y = 14
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Multiply x+y=14 by 2 and subtract from 2x-3y=18
.
2x -3y = 18
2x +2y = 28
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-5y = -10
y = 2
.
x+y = 14
x = 12
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Answer: The numbers are 2, 12, and 15.
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Always check your answer!
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Does 2x = 3y + 18?
.
2*12 = 24
3*2 = 6
6+18 = 24
Correct.
.
Is the third number minus the second number is 1 more than the first number?
z = 15
y = 2
15-2 = 13
x = 12
Yes.
.
Done.