SOLUTION: Please help me solve this word problem leading to quadractic The sum of the digits of a two-digit number is 14. The tens digit is the square of a number which is 2 less than the u

Question 992164: Please help me solve this word problem leading to quadractic
The sum of the digits of a two-digit number is 14. The tens digit is the square of a number which is 2 less than the units digit. Find the two-digit number.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
let t = the ten's digit
let u = the units
:
Write an equation for each statement
:
The sum of the digits of a two-digit number is 14.
t + u = 14
or
t = (14-u); use this form for substitution
:
The tens digit is the square of a number which is 2 less than the units digit.
t = (u-2)^2
FOIL (u-2)(u-2)
t = u^2 - 4u + 4
Replace t with (14-u)
14 - u = u^2 - 4u + 4
0 = u^2 - 4u + u + 4 - 14
A quadratic equation
u^2 - 3u - 10 = 0
Factors to
(u-5)(u+2) = 0
The positive solution is what we want here
u = 5
then
t = 14 - 5
t = 9
:
Find the two-digit number. 95
:
;
we can confirm this, in the 2nd statement
"The tens digit is the square of a number which is 2 less than the units digit."
9 = (5-2)^2
9 = 3^2
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