Question

A grocery store worker has to collect all the shopping carts left out in the parking lot. They collect 4 carts and measure the length of the 4 carts to be 51 inches. They then collect another cart for a total of 5 carts. They measure the length of the 5 carts to be 57 inches.

a. There are a total of 21 carts in the parking lot. How long will the line of 21 carts be?

b. If the grocery store worker is pushing a line of carts that is 117 inches long, how many carts do they have?

c. How long is a single cart?​

Answer 1

a. This is an Arithmetic sequence with d = 6 inches
T(5) = T(1) + 4 x 6 = 57 inches
T(1) = 57 - 24 = 33
T(21) = 33 + (21 - 1) x 6 = 153 inches

b. 33 + (n - 1) x 6 = 117
6n - 6 = 117 - 33
6n = 90
n = 15 carts

c. One cart is 33 inches long