Question

A two digit number is 5 times the sum of its digits and is also equal to 5 more than
twice the product of the digits. Find the number.
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Answer 1

Step-by-step explanation:

Let the 2 digit number be 10x+y

given: 10x+y = 5(x+y)

5x-4y 0 -(1)

Also 10xty = 5+2xy

putting y = 5x/4 from equation (1)

10x +5x/4 5 +2x(5x/4)

(45x)/4 5+ (5x2 )/2

45x 20+ 10x2

10x -45x +20 =0

2x2 -9x +4 =0

(x-4)(2x-1) = 0

hence x = 4 or 1/2

but x is an integer. so x=4

y 5x/4= 5

the number is 10x + y = 40+5-45