# The sum of the digits of the certain two-digit number is 15. while the products is 56. find the number?

2
by viki

2014-10-04T17:42:38+08:00

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So first it is a 2 digit number so think of numbers from 10-99 then if u add them its 15 and if multiplied it is 56

let x=first digit
let y=second digit

x+y=15
then the other one is
xy=15

xy=15
divide both sides by y
x=15/y

x+y=15
15/y+y=15
15/y+y^2/y=15
(15+y^2)/y=15
Multiply both sides by y
15+y^2=15y
y^2-15y+15=0
(y-8)(y-7)=0
y=7 y=8

Substitute it from first equation
x+y=15
x+7=15
x=8

x+y=15
x+8=15
x=7

There for it must be vice versa so it should be 78 where 7 is the x and 8 is the y and 87 where x is 8 and 7 is y

2014-10-05T10:52:52+08:00

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Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
8+7=15
8x7=56,
therefore: the two-digit defined is 8 and 7;