SOLUTION: The sum of two numbers is 23. the difference between three times the smaller and seven is two more than twice the larger number. find the two numbers.

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Question 161631: The sum of two numbers is 23. the difference between three times the smaller and seven is two more than twice the larger number. find the two numbers.

Answer by nerdybill(7384) (Show Source):
You can put this solution on YOUR website!
Let x = smaller number
and y = larger number
.
then from "The sum of two numbers is 23" we get:
x+y = 23 (equation 1)
.
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)
.
Solving equation 1 for y:
x+y = 23
y = 23-x
.
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)
.
substitute the above into equation 1 and solve for y:
x+y = 23
11+y = 23
y = 23-11
y = 12 (larger number)