SOLUTION: An integer is 2 less than twice another. If the product of the two integers is 220, then find the integers

Algebra ->  Problems-with-consecutive-odd-even-integers -> SOLUTION: An integer is 2 less than twice another. If the product of the two integers is 220, then find the integers      Log On


   

Question 1062092: An integer is 2 less than twice another. If the product of the two integers is 220, then find the integers
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
Integers A & B…
—
+A+=+2B-2+
+AB+=+220+
Subs from top eqn into bottom one:
+%282B-2%29B+=+220+
++2B%5E2+-+2B+=+220+
Divide everything by 2, and rearrange everything to left hand side:
+++B%5E2+-+B+-+110+=+0+
+++%28B%2B10%29%28B-11%29+=+0+
+B=-10+ or +B=11+
—
+B=-10+ —> +A+=+2%28-10%29-2+=+-22+
+B=11+ —> +A=+2%2811%29+-+2+=+20+
—
Check:
#1 if B=-10 and A=-22 :
AB = (-10)(-22) = +220 (ok)
2B-2 = 2(-10)-2 = -20 - 2 = -22 (=A) (ok)
-
#2 if +B=11+ and A=20+
AB = (11)(20) = 220 (ok)
2B-2 = 2(11) - 2 = 22-2 = 20 = A (ok)
—
—
Answer:
-10 and -22 work
and 11 and 20 work