Janine is having seven friends over for breaksfast. Of the eight people who will be eating breakfast, six like orange juice best, and two prefer grapefruit juice. Both kinds of juice cost $2.89 for half gallon, $2.09 for a quart(1/4 of a gallon), and $1.29 for a pint ( 1/8 of a gallon). How many of each size container of each type of juice should Janine buy? Use estimation to decide. Expalin the reasoning.
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To determine how many containers of each size of juice Janine should buy, we'll use estimation to get an approximate answer. Estimation involves making reasonable approximations based on the given information.
First, let's calculate the total amount of juice needed. Janine is hosting eight people, and six of them prefer orange juice, while the remaining two prefer grapefruit juice. Since each person will have the same amount of juice, we'll need 6 + 2 = 8 servings in total.
Now, let's estimate the sizes of the containers of juice needed. We have three options: half gallon, quart, and pint. Since a gallon is equal to 8 pints, we can calculate the approximate number of pints needed by dividing the number of servings by 8:
8 servings ÷ 8 = 1 pint
So, we can estimate that 1 pint of juice is needed per person. However, to be on the safe side, let's round it up to 2 pints per person.
Now, let's calculate the number of containers required for each juice type. Since there are six people who prefer orange juice,
6 people × 2 pints/person = 12 pints of orange juice
And since there are two people who prefer grapefruit juice,
2 people × 2 pints/person = 4 pints of grapefruit juice
Now, let's convert the required amounts to the available container sizes: half gallon, quart, and pint.
For orange juice:
- Half gallon (8 pints) can hold the required 12 pints.
- Quart (2 pints) can hold only 2 pints each.
- Pint (1 pint) can hold only 1 pint each.
For grapefruit juice:
- Half gallon (8 pints) can hold 4 pints.
- Quart (2 pints) can hold only 2 pints each.
- Pint (1 pint) can hold only 1 pint each.
Based on the container sizes, and considering the amount needed:
For orange juice, Janine should buy:
- 1 - Half gallon container (to hold the 12 pints)
- 6 - Quart containers (to hold the remaining 6 pints)
- 0 - Pint containers (since the quart and half-gallon containers can accommodate all the orange juice needed)
For grapefruit juice, Janine should buy:
- 1 - Half gallon container (to hold the 4 pints)
- 0 - Quart containers (as there are no quart-sized options available)
- 0 - Pint containers (as the half-gallon container can accommodate all the grapefruit juice needed)
So, the final estimation suggests that Janine should buy 1 half-gallon container of orange juice, 6 quart containers of orange juice, and 1 half-gallon container of grapefruit juice.
Note: It's important to consider the individuals' actual juice preferences and container sizes available in the market before making a final purchase decision. Estimation provides a rough approximation but may not account for exact product availability or personal preferences.