Question 163815: The sum of two integers is fifteen. Eight times the smaller is 1 less than three times the larger. Find the numbers. Answer by nerdybill(7384) (Show Source):
You can put this solution on YOUR website! I'll use the "elmination method"...
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Let x = smaller number
and
y = larger number
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Since we have two unknowns, we'll need to find two equations.
Equation 1 can be extracted from "The sum of two integers is fifteen":
x + y = 15
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Equation 2 can be extracted from "Eight times the smaller is 1 less than three times the larger.":
8x = 3y -1
rearranging:
8x - 3y = -1
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The two equations now are:
x + y = 15
8x - 3y = -1
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Multiplying the top equation by 3 to get:
3x + 3y = 45
8x - 3y = -1
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Adding the two equations together:
3x + 3y = 45
8x - 3y = -1
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11x = 44
dividing both sides by 11:
x = 4 (smaller number)
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larger number is found by substituting the above into equation 1:
x + y = 15
4 + y = 15
y = 11 (larger number)
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Ans: 4 and 11
