The product of two natural numbers is 18. If one is added to four times the smaller number this is equal to the larger number. Find both numbers

Answer 1

(4 * 2) +1 = 9

Answer 2

a = the smaller number

b = the larger number

The product of two natural numbers is 18.

This mean :

a * b = 18

If one is added to four times the smaller number this is equal to the larger number.

This mean :

1 + 4 a = b

So :

b = 1 + 4 a

Replace this value in expression :

a * b = 18

a * ( 1 + 4 a ) = 18

a + 4 a ^ 2 = 18

4 a ^ 2 + a = 18 Subtract 18 to both sides

4 a ^ 2 + a - 18 = 18 - 18

4 a ^ 2 + a - 18 = 0

The solutions are : a = - 9 / 4 and a = 2

- 9 / 4 isn't the natural number.

Solution: a = 2

b = 1 + 4 a = 1 + 4 * 2 = 1 + 8 = 9

The smaller number = 2

The larger number = 9