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Astrid is in charge of building a new fleet of ships. Each ship requires 4040 tons of wood, and accommodates 300300 sailors. She receives a delivery of 44 tons of wood each day. The deliveries can continue for 100100 days at most, afterwards the weather is too bad to allow them. Overall, she wants to build enough ships to accommodate at least 21002100 sailors. What is the number of ships Astrid can build, assuming she receives the maximum possible amount of wood?

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Q. Astrid is in charge of building a new fleet of ships. Each ship requires 4040 tons of wood, and accommodates 300300 sailors. She receives a delivery of 44 tons of wood each day. The deliveries can continue for 100100 days at most, afterwards the weather is too bad to allow them. Overall, she wants to build enough ships to accommodate at least 21002100 sailors. What is the number of ships Astrid can build, assuming she receives the maximum possible amount of wood?
  1. Calculate Total Wood: Question Prompt: How many ships can Astrid build to accommodate at least 21002100 sailors, given the wood delivery constraints?
  2. Determine Number of Ships: Calculate the total amount of wood Astrid can receive.\newlineAstrid receives 44 tons of wood each day, and deliveries can continue for 100100 days.\newlineTotal wood == Daily delivery ×\times Number of days\newlineTotal wood =4= 4 tons/day ×100\times 100 days\newlineTotal wood =400= 400 tons
  3. Calculate Total Sailors: Determine the number of ships that can be built with the total amount of wood. Each ship requires 4040 tons of wood. Number of ships =Total woodWood per ship= \frac{\text{Total wood}}{\text{Wood per ship}} Number of ships =400 tons40 tons/ship= \frac{400 \text{ tons}}{40 \text{ tons/ship}} Number of ships =10= 10 ships
  4. Check Sailor Requirement: Calculate the total number of sailors that can be accommodated by the ships built.\newlineEach ship accommodates 300300 sailors.\newlineTotal sailors == Number of ships ×\times Sailors per ship\newlineTotal sailors =10= 10 ships ×300\times 300 sailors/ship\newlineTotal sailors =3000= 3000 sailors
  5. Check Sailor Requirement: Calculate the total number of sailors that can be accommodated by the ships built. Each ship accommodates 300300 sailors. Total sailors == Number of ships ×\times Sailors per ship Total sailors =10= 10 ships ×300\times 300 sailors/ship Total sailors =3000= 3000 sailors Check if the number of sailors that can be accommodated meets the requirement. Astrid wants to build enough ships to accommodate at least 21002100 sailors. Since 30003000 sailors > 21002100 sailors, the requirement is met.

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