You are planning the layout for a new supermarket.

Question

You need to know how much space should be reserved in the parking lot and in the store entrance for shopping carts. shopping carts can "nest", or fit partially inside each other.

a) if one cart has a lenght of 3 feet, and a stack of 12 nested carts is 16.75 feet long, how much of each cart is inside another when they are "nested"?

b)what woould the length of a 20-cart stack be?

c)write an equation that gives the length, L, of a stack of n shopping carts.

d)is it possible to have a nested stack of carts that is exactly 30 ft. long? explain your reasoning.

 

i would like to focus more on letter D which is the one I'm confused on thank you

Answer 1

The way I see it, when the carts are "nested", they all effectively have a shorter length except for the last one that is sticking out on the end. So,

a) 12 nested carts are equivalent to 11 shortened carts and one full cart. Subtract 3 feet for the one full cart, and the remaining 11 shortened carts have a combined length of 13.75 feet. Divide that by the 11 carts for a per-cart shortened length of 1.25 feet. This means that each cart has the remaining 1.75 feet inside the next cart when they are "nested".

b) A 20-cart stack would be 19 shortened carts plus one full cart, for a total of 19 * 1.25 + 3 = 26.75 feet.

c) Based on the above work, we can say that L = 1.25(n-1) +3 , where n is the number of carts and L is the total length of the nested stack.

d) Set 30 = 1.25(n-1) + 3, so that 27 = 1.25(n-1), and thus n = 22.6, which is NOT a whole number. So, therefore, no number of carts can equal exactly 30 feet in a "nested" arrangement. 22 carts would be shorter (at 29.25 feet) and 23 carts would be too long (at 30.5 feet).