Question 161631
Let x = smaller number
and y = larger number
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then from "The sum of two numbers is 23" we get:
x+y = 23 (equation 1)
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and from "the difference between three times the smaller and seven is two more than twice the larger number." we get
3x-7 = 2y+2 (equation 2)
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Solving equation 1 for y:
x+y = 23
y = 23-x
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substitute this into equation 2 and solve for x:
3x-7 = 2y+2 
3x-7 = 2(23-x)+2 
3x-7 = 46 - 2x + 2 
5x-7 = 48
5x = 55
x = 11 (smaller number)
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substitute the above into equation 1 and solve for y:
x+y = 23
11+y = 23
y = 23-11
y = 12 (larger number)