A catcher's and a pitcher's uniform numbers are consecutive integers whose product is 306. If the catcher's was the smaller number, determine the uniform number of each player. catcher's number pitcher's number

Catcher's number = 17

Pitcher's number = 18

Step-by-step explanation:

Let two consecutive numbers be represented by x and (x + 1)

Hence, their product

= x (x + 1) = 306

= x² + x - 306 = 0

We factorise

= x² + 18x - 17x - 306 = 0

= x (x + 18) - 17 (x + 18) = 0

= (x + 18) (x - 17) = 0

x + 18 = 0 = - 18

x - 17 = 0 = 17

x = 17 and - 18

Our answer can't be a negative integer

Hence x = 17

The second consecutive integer = x + 1

= 17 + 1 = 18

Hence the uniform numbers are 17 and 18.

We are told in question that: If the catcher's was the smaller number, determine the uniform number of each player.

Therefore,

The Catcher's uniform number = 17

The Pitcher's uniform number = 18