Final answer:
To find the maximum number of bottles of pineapple juice, we need to determine the cost of the pineapple juice and soda water, and compare it to the amount of money available. The inequality 8.2x ≤ 41 can be used to solve for x, which represents the number of bottles of pineapple juice. The answer is 5 bottles.
Step-by-step explanation:
To find out how many bottles of pineapple juice Alex can buy, we need to determine the cost of the pineapple juice and the soda water. Then, we can compare the total cost to the amount of money Alex has.
Given that pineapple juice costs $3.70 per bottle and soda water costs $1.80 per bottle, and the recipe calls for 2.5 times as many bottles of soda water as pineapple juice, we can set up the equation:
Cost of pineapple juice + Cost of soda water = Total cost
Let x be the number of bottles of pineapple juice. Then, the number of bottles of soda water would be 2.5x.
The cost of the pineapple juice is 3.7x and the cost of the soda water is 1.8(2.5x) = 4.5x.
The total cost is 3.7x + 4.5x = 8.2x.
Now, we can set up the inequality 8.2x ≤ 41 to represent the fact that Alex can only spend a maximum of $41.
Solving the inequality, we find that x ≤ 5.
Therefore, Alex can buy at most 5 bottles of pineapple juice if he only has $41.00.