SOLUTION: the sum of two intergers is 10. Three times the larger interger is three less than eight times the smaller integer. Find the integers.

Question 212816: the sum of two intergers is 10. Three times the larger interger is three less than eight times the smaller integer. Find the integers.
Found 2 solutions by ankor@dixie-net.com, Earlsdon:
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
the sum of two integers is 10.
x + y = 10
y = (10-x)
;
Three times the larger integer is three less than eight times the smaller integer.
3x = 8y - 3
:
Find the integers.
Substitute (10-x) for y in the above equation and find x
3x = 8(10-x) - 3
3x = 80 - 8x - 3
:
See if you can do it now
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
Let the larger integer be a and the smaller integer, b, then:
1) a+b = 10 "The sum of two integers is 10."
2) 3a = 8b-3 "Three times the larger...is three less than eight times the smaller..."
Rewrite equation 1 as a = 10-b and substitute into equation 2, then solve for b.
3(10-b) = 8b-3 Expand the left side.
30-3b = 8b-3 Add 3b to both sides.
30 = 11b-3 Add 3 to both sides.
33 = 11b Finally, divide both sides by 11.
3 = b and a = 10-3 = 7.
The two integers are:
7 and 3
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