SOLUTION: the sum of two numbers is 22 and their product is 120. Find the two numbers

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Question 938365: the sum of two numbers is 22 and their product is 120. Find the two numbers
Found 2 solutions by Fombitz, MathLover1:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
A%2BB=22
A%2AB=120
From the first equation,
A=22-B
Substitute into the second,
%2822-B%29B=120
22B-B%5E2=120
B%5E2-22B%2B120=0
%28B-12%29%28B-10%29=0
Two solutions,
B-12=0
B=12
then,
A=22-12=10
and
B-10=0
B=10
then,
A=22-10=12
10 and 12 are the numbers.

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

let the two numbers be x and y
if the sum of two numbers is 22, then we have
x%2By=22......eq.1
if their product is 120, we have

x%2Ay=120......eq.2
solve the system:
x%2By=22......eq.1
x%2Ay=120......eq.2
_______________________
start with
x%2By=22......eq.1 ...solve for x
x=22-y...substitute in eq.2
%2822-y%29%2Ay=120......eq.2...solve for y
22y-y%5E2=120
0=y%5E2-22y%2B120
0=y%5E2-2y-10y%2B120
0=%28y%5E2-2y%29-%2810y-120%29
0=y%28y-2%29-10%28y-12%29
%28y-12%29%28y-10%29=0
solutions:
%28y-12%29=0=>y=12
or
%28y-10%29=0=>y=10
now find x:
x=22-y=>x=22-12=>x=10
x=22-y=>x=22-10=>x=12
so, your numbers are:
x=10 and y=12
or
x=12 and y=10