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Question 52053: The sum of 2 integers is 10. Three times the larger is three less than 8 times the smaller. Find the integers
Answer by Earlsdon(6294)   (Show Source):
You can put this solution on YOUR website! Try this:
Let a = the larger integer and b = the smaller integer.
From the problem description, you can write:
1) a + b = 10 (The sum of the integers is 10) and
2) 3a = 8b-3 (Three times the larger (3a) is (=) 8 times the smaller (8b) less three (-3).
Rewrite equation 1) as:
b = 10-a, substiute this into equation 2) and solve for a.
2a) 3a = 8(10-a)-3 Simplify.
2b) 3a = 80-8a-3
2c) 3a = 77-8a Add 8a to both sides of the equation.
2)d 11a = 77 Divide both sides by 11.
2e) a = 7 This is the larger number.
b = 10-a
b = 10-7
b = 3 This is the smaller number.
Check:
a+b = 7+3 = 10 OK
3a = 8b-3
3(7) = 8(3)-3
21 = 24-3
21 = 21 OK
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