SOLUTION: Find two integers whose product is 78 such that one of the integers is five less than three times the other integer. smaller number: larger number: I got: y=-6 and y=13/3

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Find two integers whose product is 78 such that one of the integers is five less than three times the other integer. smaller number: larger number: I got: y=-6 and y=13/3       Log On


   



Question 846903: Find two integers whose product is 78 such that one of the integers is five less than three times the other integer.
smaller number:
larger number:
I got: y=-6 and y=13/3 from the factors (3y-13) and (y+6).
Thank you for your help!

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let the integers = +x+ and +y+
given:
(1) +y%2Ax+=+78+
(2) +y+=+3x+-+5+
------------------------
Substitute (2) into (1)
(1) +%28+3x+-+5+%29%2Ax+=+78+
(1) +3x%5E2+-+5x+=+78+
(1) +3x%5E2+-+5x+-+78+=+0+
Use quadratic formula
+x+=+%28+-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+3+
+b+=+-5+
+c+=+-78+
+x+=+%28+-%28-5%29+%2B-+sqrt%28+%28-5%29%5E2+-+4%2A3%2A%28-78%29+%29%29+%2F+%282%2A3%29+
+x+=+%28+5+%2B-+sqrt%28+25+%2B+936+%29%29+%2F+6+
+x+=+%28+5+%2B+sqrt%28+961+%29%29+%2F+6+
+x+=+%28+5+%2B+31+%29+%2F+6+
+x+=+36%2F6+
+x+=+6+
and
(2) +y+=+3x+-+5+
(2) +y+=+3%2A6+-+5+
(2) +y+=+18+-+5+
(2) +y+=+13+
The integers are 6 and 13
check:
(1) +y%2Ax+=+78+
(1) +13%2A6+=+78+
(1) +78+=+78+
OK