A=2 cups concentarte:3 cups water

B=5 cups concentrate:9 cups water
C=1 cup concentrate:2 cups water
D=3 cups concentrate:5 cups water

For each mix, how many batches are needed to make juice for 240 campers? (each camper gets half a cup of juice)

Please check the advice that Reiny and I each gave you. Note that the problem that Reiny answered is slightly different.

http://www.jiskha.com/display.cgi?id=1227199729

http://www.jiskha.com/display.cgi?id=1227132102

As I recall, you have all of them correct except for B.

To determine the number of batches needed for each mix to make juice for 240 campers, we need to compare the concentration of each mix with the desired concentration of juice per camper.

Given:
A is 2 cups concentrate:3 cups water (concentration = 2/(2+3) = 2/5)
B is 5 cups concentrate:9 cups water (concentration = 5/(5+9) = 5/14)
C is 1 cup concentrate:2 cups water (concentration = 1/(1+2) = 1/3)
D is 3 cups concentrate:5 cups water (concentration = 3/(3+5) = 3/8)

We want each camper to get half a cup of juice, which means the concentration of the juice should be 1/2.

Let's calculate the number of batches needed for each mix to reach the desired concentration of 1/2:

A:
Ratio needed = 1/2
Ratio of concentrate to total = 2/5
Number of batches needed = (Ratio needed) / (Ratio of concentrate to total)
= (1/2) / (2/5)
= (1/2) * (5/2)
= 5/4
= 1.25 batches

B:
Ratio needed = 1/2
Ratio of concentrate to total = 5/14
Number of batches needed = (Ratio needed) / (Ratio of concentrate to total)
= (1/2) / (5/14)
= (1/2) * (14/5)
= 7/5
= 1.4 batches

C:
Ratio needed = 1/2
Ratio of concentrate to total = 1/3
Number of batches needed = (Ratio needed) / (Ratio of concentrate to total)
= (1/2) / (1/3)
= (1/2) * (3/1)
= 3/2
= 1.5 batches

D:
Ratio needed = 1/2
Ratio of concentrate to total = 3/8
Number of batches needed = (Ratio needed) / (Ratio of concentrate to total)
= (1/2) / (3/8)
= (1/2) * (8/3)
= 4/3
= 1.3333 batches (approximately)

Thus, the number of batches needed for each mix to make juice for 240 campers (each camper gets half a cup of juice) are as follows:

A: 1.25 batches
B: 1.4 batches
C: 1.5 batches
D: 1.3333 batches (approximately)

To determine the number of batches needed for each mix to make juice for 240 campers, we need to calculate the total volume of juice required and divide it by the volume of juice produced in each batch.

First, let's determine the total volume of juice required. Since each camper gets half a cup of juice, we need to multiply the number of campers by 0.5 to get the total volume:

Total volume of juice = Number of campers * Volume per camper
Total volume of juice = 240 * 0.5
Total volume of juice = 120 cups

Now, let's calculate the number of batches needed for each mix.

For mix A (2 cups concentrate: 3 cups water), the total volume of juice produced in each batch is 2 + 3 = 5 cups.
Number of batches = Total volume of juice required / Volume per batch
Number of batches = 120 cups / 5 cups
Number of batches = 24 batches

For mix B (5 cups concentrate: 9 cups water), the total volume of juice produced in each batch is 5 + 9 = 14 cups.
Number of batches = Total volume of juice required / Volume per batch
Number of batches = 120 cups / 14 cups (approximately)
Number of batches = 8.57 batches (rounded up to the nearest whole number)
Number of batches = 9 batches (rounded up)

For mix C (1 cup concentrate: 2 cups water), the total volume of juice produced in each batch is 1 + 2 = 3 cups.
Number of batches = Total volume of juice required / Volume per batch
Number of batches = 120 cups / 3 cups
Number of batches = 40 batches

For mix D (3 cups concentrate: 5 cups water), the total volume of juice produced in each batch is 3 + 5 = 8 cups.
Number of batches = Total volume of juice required / Volume per batch
Number of batches = 120 cups / 8 cups
Number of batches = 15 batches

Therefore, to make juice for 240 campers with each camper getting half a cup of juice, we would need:
- 24 batches for mix A
- 9 batches for mix B
- 40 batches for mix C
- 15 batches for mix D