School cafeteria has a juice dispenser that holds 640 lid ounces of juice when completely filled. Juice is offered in two serving sizes: 4 ounces or 8 ounces.
Each day, approximately 7 out of 10 students choose the 4-ounce serving size, and the other students choose the 8-ounce serving size.
If 7 out of 10 students choose the 4-ounce serving size, then the remaining 3 out of 10 students choose the 8-ounce serving size.
Let's calculate the number of students choosing each serving size:
- Number of students choosing 4-ounce serving size = 7/10 * total number of students
- Number of students choosing 8-ounce serving size = 3/10 * total number of students
We can represent the above calculations with the following equations:
- Number of students choosing 4-ounce serving size = (7/10) * N
- Number of students choosing 8-ounce serving size = (3/10) * N
where N represents the total number of students.
Now, let's calculate the total amount of juice consumed per day:
- Total amount of juice consumed by students choosing 4-ounce serving size = (7/10) * N * 4
- Total amount of juice consumed by students choosing 8-ounce serving size = (3/10) * N * 8
Adding both amounts, we get the total amount of juice consumed by all students:
Total juice consumed = (7/10) * N * 4 + (3/10) * N * 8
Given that the juice dispenser holds 640 lid ounces, we can set the total juice consumed equal to the dispenser capacity:
(7/10) * N * 4 + (3/10) * N * 8 = 640
Solving this equation will give us the total number of students, N.