SOLUTION: The product of two numbers is 96. One number is 4 more than the other number. Find the two numbers.

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Question 1049902: The product of two numbers is 96. One number is 4 more than the other number. Find the two numbers.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

let numbers be x and y
if the product of two numbers is 96, we have
xy=96........solve for x
x=96%2Fy...............eq.1
if one number is 4 more than the other number, we have
x=y%2B4.........eq.2
from eq.1 and eq.2 we have
96%2Fy=y%2B4........solve for y
96=y%28y%2B4%29
96=y%5E2%2B4y
y%5E2%2B4y-96=0.............use quadratic formula

y+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+...since a=1,b=4, and c=-96 we have

y+=+%28-4+%2B-+sqrt%28+4%5E2-4%2A1%2A%28-96%29+%29%29%2F%282%2A1%29+
y+=+%28-4+%2B-+sqrt%28+16%2B384+%29%29%2F2+
y+=+%28-4+%2B-+sqrt%28+400+%29%29%2F2+
y+=+%28-4+%2B-+20%29%2F2+
y+=+%28-cross%284%292+%2B-+cross%2820%2910%29%2Fcross%282%291+
y+=+%28-2+%2B-+10%29+
solutions:
y+=+-2+%2B+10+->y+=+8+
or
y+=+-2-+10+->y+=+-12+
now find corresponding x for each y
x=y%2B4.........eq.2...if y+=+8+
x=8%2B4
x=12
x=y%2B4.........eq.2...if y+=+-12+
x=-12%2B4
x=-8

so, we have two solutions:
1.x=12 and y+=+8+
2.x=-8 and y+=+-12+