Mixture Problem

rnaah wrote:According to the directions on a can of frozen orange juice concentrate, 1 can of concentrate is to be mixed with 3 cans of water to make orange juice. How many 12-ounce cans of the concentrate are required to prepare 200 6-ounce servings of orange juice?

TO prepare 200 6-ounce servings would mean 1200 ounce of juice, this would mean 300 ounce concentrate and 900 ounce water.
So we need 300 ounce of concentrate.
cans = 300/12=25 cans.

Cheers
Ami/-

rnaah wrote:According to the directions on a can of frozen orange juice concentrate, 1 can of concentrate is to be mixed with 3 cans of water to make orange juice. How many 12-ounce cans of the concentrate are required to prepare 200 6-ounce servings of orange juice?

Let C = concentrate and W = water.
Since 1 can of concentrate is needed for every 3 cans of water, C:W = 1:3.
Use a ratio box:

____________C____W____Total

Ratio:_______1____3_____4

Multiplier:

Actual:_________________1200

In the top row, put the ratio (C:W = 1:3).
The last column is the total: 1+3 = 4.
In the bottom row, put any known values.
The total volume of juice to be produced = 200*6 = 1200 ounces.
Put this value in the bottom right box under "Total".

To determine the middle row -- the multiplier -- divide the known actual value (1200) by its corresponding value in the top row (4):
1200/4 = 300.
The multiplier is placed in every column along the middle row:

____________C____W____Total

Ratio:_______1____3______4

Multiplier:__300__300____300

Actual:_________________1200


Now complete the box by multiplying every value in the top row by the multiplier:

____________C_____W______Total

Ratio:_______1____3______4

Multiplier:__300__300____300

Actual:_____300__900____1200

Thus, the amount of concentrate needed = 300 ounces.
Since each can is 12 ounces, the number of cans needed = 300/12 = 25.

rnaah wrote:According to the directions on a can of frozen orange juice concentrate, 1 can of concentrate is to be mixed with 3 cans of water to make orange juice. How many 12-ounce cans of the concentrate are required to prepare 200 6-ounce servings of orange juice?

Since this talks about mixtures in small portions & a unknown value in a large portion, we should use ratios to solve this.


Concrt : Water : Juice

1 : 3 : 4 (in cans)

? : ? : 1200 (6 x 200) (in ounces)

so we know the multiplying factor is 300 (i.e. 4 x 300 = 1200)
& we use it for the rest
300 : 900 : 1200 (in ounces)

since 12 ounces = 1 can
300 ounces = 300/12 = 25 cans of concentrate