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. How much wood does Astrid need to accommodate 2100 sailors?
Step 1: Determine how many sailors a single ship can accommodate.
According to the provided information, each ship accommodates 300 sailors.
Step 2: Calculate how many ships are needed to accommodate 2100 sailors.
Since every ship can accommodate 300 sailors, you would use the formula:
Number of Ships (NS) needed = Total number of sailors / sailors per ship
NS = 2100 sailors / 300 sailors per ship
NS = 7 ships
Step 3: Determine how much wood is needed for one ship.
We're given each ship requires 40 tons of wood.
Step 4: Calculate how much wood Astrid needs total to build the number of ships calculated in step 2.
Using the formula:
Total Wood needed = Number of Ships * Wood per ship
Total Wood = 7 ships * 40 tons of wood/ship
Total Wood = 280 tons of wood
So, Astrid needs 280 tons of wood to accommodate 2100 sailors.
For Verification:
Let's verify the solution by calculating how many sailors can be accommodated with 280 tons of wood.
Step 1: Calculate how many ships can be built with 280 tons of wood.
Total Ships = Total Wood / Wood per ship
Total Ships = 280 tons of wood / 40 tons of wood/ship
Total Ships = 7 ships
Step 2: Calculate how many sailors can be accommodated with the 7 ships found.
Total sailors = Total Ships * Sailors per ship
Total sailors = 7 ships * 300 sailors/ship
Total sailors = 2100 sailors
As this matches the number initially stated in the problem (2100 sailors), we can conclude that our original calculation was done correctly.
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