Question
Mr burr the head custodian is working on putting new numbers on 42 of the 81 classroom doors. He found two numbers for the 23rd door he was working on in the 6th grade hallway whose sum is 35 and their product is 306. What are the two numbers?
Answers
Henry
Eq1: X+Y = 35.
Eq2: XY.
X + Y = 35
Y = 35-X
In Eq2, replace Y with 35-X
X(35-X) = 306
-X^2 + 35x = 306
-X^2 + 35x - 306 = 0.
X^2 _ 35 + 306 = 0
(x-17)(x-18) = 0.
X = 17, and 18.
Eq2: XY.
X + Y = 35
Y = 35-X
In Eq2, replace Y with 35-X
X(35-X) = 306
-X^2 + 35x = 306
-X^2 + 35x - 306 = 0.
X^2 _ 35 + 306 = 0
(x-17)(x-18) = 0.
X = 17, and 18.
Henry
Correction:
Eq2: XY = 306.
Eq2: XY = 306.