A two digit number is four times

Question

the sum of the digitsand twice the product of the digits.find the number?

Answer 1

Let the digits be a, b.

Four times the sum of digits = 4(a + b).

Twice the product of the digits = 2(ab).

4(a + b) = 2(ab)

2(a + b) = (ab)     ------- (1)

"the number is four times the sum of its digits"

10a+b =4(a + b)

10a+b =4a+4b

6a =3b

b=2a

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Substitute 2a for b in equation (1)

2(a + b) = (ab)

2(a + 2a) = (a(2a))

6a =2a²

2a = 6

a =3

b=2(3) =6

Therefore, the number is 10(3)+6 =36