SOLUTION: Please help me solve: The distance between two numbers is 18. Twice the smaller plus three times the larger is 74. What are the numbers? Thank you.

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Question 213614This question is from textbook Intoductery Algebra
: Please help me solve:
The distance between two numbers is 18. Twice the smaller plus three times the larger is 74. What are the numbers?
Thank you. This question is from textbook Intoductery Algebra

Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
The distance between two numbers is 18. Twice the smaller plus three times the larger is 74. What are the numbers?
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Let the larger be "x":
Let the smaller be "y":
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Equations:
x-y = 18
2y+3x = 74
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Rearrange the 1st equation:
x = y+18
Substitute into the 2nd equation to solve for "y";
2y + 3(y+18) = 74
2y + 3y + 54 = 74
5y = 20
y = 4 (the smaller number)
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Since x = y+18, x = 4+18 = 22 (the larger number)
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Cheers,
Stan H.