A two-digit number is such that the product of the digits is 8 .when 18 is added to the number, then the digits are reversed.the number is
Answers
Answer:the answer is 24.
Step-by-step explanation:let unit,s digit be y and tens digit be x ,then
xy=8 ————-(1)
yx=xy+18 ———(1)
from equation 2 by simplifying it ,we get:-
10y+x=10x +y +18
9y=9x+18 ,then divide both side of the equation by 9
y=x+2 ————-(3)
from equations 1 and 3 by substituting y by x+2 ,we get:-
xy=8 , x(x+2) =8
x2+2x=8 , x2+2x-8=0
then we solve the quadratic equation for what method that is easy for you either by completing square ,factoring method or by formula
now I am using by factoring
x2+2x-8=0
x2+4x-2x-8=0
x(x+4)-2(x+4) =0
(x+4)(x-2) =0
x+4=0 ,x-2=0
x=-4 , x=2
we omitted negative number and took positive integer that is x=2
then, y=y=x+2 =2+2=4
the number is the form of (xy) =24
Therefore the number is 24
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