Astrid is in charge of building a new fleet of ships. Each ship requires $40$ tons of wood, and accommodates $300$ sailors. She receives a delivery of $4$ tons of wood each day. The deliveries can continue for $100$ days at most, afterwards the weather is too bad to allow them. Overall, she wants to build enough ships to accommodate at least $2100$ sailors. $\newline$ What is the number of ships Astrid can build, assuming she receives the maximum possible amount of wood? $\newline$ ships

Full solution

Q. Astrid is in charge of building a new fleet of ships. Each ship requires

40

tons of wood, and accommodates

300

sailors. She receives a delivery of

4

tons of wood each day. The deliveries can continue for

100

days at most, afterwards the weather is too bad to allow them. Overall, she wants to build enough ships to accommodate at least

2100

sailors.

\newline

What is the number of ships Astrid can build, assuming she receives the maximum possible amount of wood?

\newline

ships

Calculate total wood: Calculate the total amount of wood Astrid can receive. $\newline$ Astrid receives $4$ tons of wood each day for $100$ days. $\newline$ Total wood $= 4 \text{ tons/day} \times 100 \text{ days}$ $\newline$ Total wood $= 400$ tons
Determine number of ships: Determine how many ships can be built with the total amount of wood. $\newline$ Each ship requires $40$ tons of wood. $\newline$ Number of ships $= \frac{\text{Total wood}}{\text{Wood per ship}}$ $\newline$ Number of ships $= \frac{400 \text{ tons}}{40 \text{ tons/ship}}$ $\newline$ Number of ships $= 10$ ships
Calculate total sailors accommodated: Calculate the total number of sailors that can be accommodated by the ships built. $\newline$ Each ship accommodates $300$ sailors. $\newline$ Total sailors accommodated $=$ Number of ships $\times$ Sailors per ship $\newline$ Total sailors accommodated $=$ $10$ ships $\times$ $300$ sailors/ship $\newline$ Total sailors accommodated $=$ $3000$ sailors
Check sailor requirement: Check if the total number of sailors accommodated meets Astrid's requirement. $\newline$ Astrid wants to accommodate at least $2100$ sailors. $\newline$ Since $3000$ sailors $>$ $2100$ sailors, Astrid's requirement is met.