SOLUTION: The sum of two integers is fifteen. Eight times the smaller is 1 less than three times the larger. Find the numbers.

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"...
.
Let x = smaller number
and
y = larger number
.
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
.
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
.
The two equations now are:
x + y = 15
8x - 3y = -1
.
Multiplying the top equation by 3 to get:
3x + 3y = 45
8x - 3y = -1
.
Adding the two equations together:
3x + 3y = 45
8x - 3y = -1
-------------
11x = 44
dividing both sides by 11:
x = 4 (smaller number)
.
larger number is found by substituting the above into equation 1:
x + y = 15
4 + y = 15
y = 11 (larger number)
.
Ans: 4 and 11
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