A small airplane can carry passengers, luggage, and mail as long as their total weight is less than $1,700$ pounds. Tuesday's load of mail weighs $490$ pounds. If the average combined weight of each passenger and their luggage is $170$ pounds, what is the greatest possible number of passengers that can travel on the airplane on Tuesday? $\newline$ Choose $1$ answer: $\newline$ (A) $7$ $\newline$ (B) $8$ $\newline$ (C) $10$ $\newline$ (D) $12$

Full solution

Q. A small airplane can carry passengers, luggage, and mail as long as their total weight is less than

1,700

pounds. Tuesday's load of mail weighs

490

pounds. If the average combined weight of each passenger and their luggage is

170

pounds, what is the greatest possible number of passengers that can travel on the airplane on Tuesday?

\newline

Choose

1

answer:

\newline

(A)

7

\newline

(B)

8

\newline

(C)

10

\newline

(D)

12

Determine Weight Limit: Determine the total weight allowed for passengers and their luggage. The total weight the airplane can carry is $1,700$ pounds, and the mail weighs $490$ pounds. Subtract the weight of the mail from the total weight to find the remaining weight available for passengers and their luggage. Calculation: $1700$ pounds $-$ $490$ pounds $=$ $1210$ pounds
Calculate Maximum Passengers: Calculate the maximum number of passengers that can be carried based on the average weight. $\newline$ The average combined weight of each passenger and their luggage is $170$ pounds. $\newline$ Divide the remaining weight available by the average weight per passenger to find the maximum number of passengers. $\newline$ Calculation: $1210$ pounds $/$ $170$ pounds per passenger $=$ $7.11764706$
Round Down Passengers: Determine the greatest whole number of passengers that can travel. Since we cannot have a fraction of a passenger, we need to round down to the nearest whole number. The greatest whole number of passengers is $7$ .