SOLUTION: The product of a two-digit number and its tens digit is 285. The units digit is two more than the tens digit. What is the original number?

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Question 194932This question is from textbook Algebra and Trigonometry Structure and Method Book 2
: The product of a two-digit number and its tens digit is 285. The units digit is two more than the tens digit. What is the original number? This question is from textbook Algebra and Trigonometry Structure and Method Book 2

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = the 10's digit
Let y = the units
then
10x + y = the two digit number
;
"The product of a two-digit number and its tens digit is 285".
x(10x + y) = 285
:
" The units digit is two more than the tens digit."
y = x+2
:
Substitute (x+2) for y in the 1st equation
x(10x + (x+2)) = 285
:
x(11x + 2) = 285
:
11x^2 + 2x = 285
:
11x^2 + 2x - 285 = 0; a quadratic equation
Factors to:
(11x + 57)(x - 5) = 0
Positive solution
x = 5
then
y = 5 + 2
y = 7
:
the original number = 57
;
:
Check solution:
5(10(5) + 7) =
5(57) = 285