The manager at Sunshine Days Camp is going to buy juice for the campers. Each bottle contains 64 ounces of juice. Each camper is expected to drink more than 11 ounces of juice. There are 72 campers.
(a)Explain how the manager would write an inequality to represent the number of ounces of juice,j,that she should buy.
(b)What is the least number of bottles of juice the manager can buy to have at least this much juice? Explain.
(a) To write an inequality to represent the number of ounces of juice the manager should buy, we need to consider the amount of juice each camper is expected to drink and the total number of campers.
Since each camper is expected to drink more than 11 ounces of juice, we can represent this by the inequality: j > 11.
The total number of ounces of juice needed would be the product of the number of campers (72) and the amount of juice each camper is expected to drink (11): j > 72 * 11.
Simplifying the inequality, we get: j > 792.
Therefore, the inequality the manager would write to represent the number of ounces of juice she should buy is j > 792.
(b) To find the least number of bottles of juice the manager can buy to have at least this much juice, we need to divide the total number of ounces of juice needed by the number of ounces in each bottle.
The total number of ounces of juice needed is 792 (as determined by the inequality j > 792).
Since each bottle contains 64 ounces of juice, we divide 792 by 64 to find the least number of bottles needed: 792 / 64 = 12.375.
However, since we cannot buy a fraction of a bottle, we must round up to the next whole number.
Therefore, the least number of bottles of juice the manager can buy to have at least this much juice is 13.
(a) To represent the number of ounces of juice, j, that the manager should buy, she would write the following inequality:
j ≥ number of campers × ounces of juice per camper
In this case, the number of campers is 72 and the ounces of juice per camper is 11. Therefore, the inequality becomes:
j ≥ 72 × 11
(b) To find the least number of bottles of juice the manager can buy to have at least this much juice, we need to calculate the total amount of juice required. The equation for this is:
total amount of juice required = number of campers × ounces of juice per camper
In this case, the number of campers is 72 and the ounces of juice per camper is 11. Therefore:
total amount of juice required = 72 × 11 = 792 ounces
Since each bottle contains 64 ounces of juice, the manager needs to buy enough bottles to have at least 792 ounces of juice. The least number of bottles she can buy to have at least this much juice is:
least number of bottles = total amount of juice required ÷ ounces of juice per bottle
In this case:
least number of bottles = 792 ÷ 64 = 12.375
Since the manager cannot buy a fraction of a bottle, she should buy at least 13 bottles of juice.