The manager of a summer camp has 14 baseballs and 23 tennis

The manager of a summer camp has 14 baseballs and 23 tennis balls. The manager buys some boxes of baseballs with 12 baseballs to a box and an equal number of boxes of tennis balls with 16 tennis balls to a box. Write an expression to represent the total number of balls. Write expressions for the total number of baseballs and tennis balls. Let n represent the number of boxes of each type. baseballs: n tennis balls: n Find an expression for the total number of balls. Combine the two expressions. Use the Commutative Property. Combine like terms. So, the total number of baseballs and tennis balls is

Solution

STEP 1 :

For each box contain 12 base balls and the manager have total 14 base balls.

so the expression for base balls : 2 + (12)n    (for n = 1)

for tennis balls total 23 balls are there and each box contain 16 balls.

so the expression for tennis balls : 7 + (16)n (for n = 1)

STEP 2 :

combining two expressions

2 + (12)n + 7 + (16)n

2 + 7 + (12 + 16)n

9 + (28)n

so total number of base balls and tennis balls is 9 + (28)n

here n representing the number of boxes.

so for n=1 we will have 9 + (28)1 = 9 + 28 = 37

so total number of base balls and tennis balls is 14+23 = 37