Question

The manager of a summer camp had 15 baseballs and 21 tennis balls. The manager buys some boxes of baseballs with 16 baseballs to a box and an equal number of boxes of tennis balls with 11 tennis balls to a box. Let n represent the number of boxes of each type. Select the algebraic expression for the total number of balls.

a) 15 + 16n
b) 21 + 11n
c) 36 + 27n
d) 16n + 11n

Answer 1

The correct algebraic expression for the total number of balls, accounting for the initial balls and additional purchased boxes, is 36 + 27n, which is option c).

Step-by-step explanation:

The student is asked to select the algebraic expression representing the total number of balls. Initially, there are 15 baseballs and 21 tennis balls. Boxes of baseballs contain 16 balls each, and boxes of tennis balls contain 11 balls each. The variable n represents the number of boxes bought for each type of ball.

To find the total number of balls, you must add the initial number of balls to the product of the number of boxes and the number of balls per box, for each type of ball. The expression will be the sum of the initial number of baseballs and the product of the number of baseball boxes bought (16n) plus the initial number of tennis balls and the product of the number of tennis ball boxes bought (11n).

Therefore, the correct algebraic expression for the total number of balls is 15 + 16n + 21 + 11n. Combining like terms gives us 36 + 27n, which corresponds to option c).