Problem Solving

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?

A) 25
B) 34
C) 50
D) 67
E) 100

*** Answer should be A ***

Thanks in advance!

adi 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?

A) 25
B) 34
C) 50
D) 67
E) 100

*** Answer should be A ***

Thanks in advance!

For every 1 oz of concentrate, we'll make 4 oz of OJ (since we mix that 1oz of concentrate with 3 oz of water).

The question asks how many 12oz cans of concentrate we'll need to make a total of 1200 oz of OJ.

Since concentrate makes up 1/4 of the OJ, we know that 300oz of the 1200 oz will be concentrate.

So, we have 300oz/(12oz/1can) = 25 cans.

This would also be a great candidate for backsolving, i.e. working backwards from the answer choices.

DO YOU THINK THIS IS A 600-700 level question?

Another way to thing about this question:

1 oz of concentrate + 3oz water = 4 oz of OJ

the question is asking how many 12oz cans of concentrate we'll need to make a total 200-6oz. OR 100-12oz ?

1 oz of concentrate + 3 oz water = 4 oz of OJ
? oz of concentrate + ? oz water = 100 oz of OJ

100/4 or 4 * 25 = 100

so, 1 oz of concentrate * 25 = 25 oz of concentrate
and, 3 oz water * 25 = 75 oz of water

Is there an easier approach to this???

I find it too difficult computing this in under 2 mins.

I don't get this...

Can someone explain once more with a step by step approach?

KICKGMATASS123 wrote:I don't get this...

Can someone explain once more with a step by step approach?

Not really. The easiest way is to see that you will have 1200oz of OJ. That consists of 4*12oz cans of mix.

1200/48 = 25 cans

or

realize that the concentrate is 1/4 of the total ounces
1/4 of 1200 is 300oz of concentrate

Finally
300oz/12 = 25 cans

KICKGMATASS123 wrote:I don't get this...

Can someone explain once more with a step by step approach?

The goal is to mantain the ratio 1C/3W=orange juice. So Orange juice is composed of 1ozConcentrate and 3ozWater. If you have 200 6 oz equals 1200oz. Divide by 4 to know how many oz of Concentrate you have in 1200oz. So 1200/4= 300ozCon 900ozW . As the can of Concetrate have 12oz we must divide the total oz of Concentrate 300 by 12oz= 25 (12 ounce cans of concentrate).

adi 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?

A) 25
B) 34
C) 50
D) 67
E) 100

*** Answer should be A ***

Thanks in advance!

1 can of frozen OJ+3 cans of water = 4 oz. OJ

Since we are trying to find 6 oz. OJ servings instead of 1 oz. OJ servings, split the 4 oz. OJ in half, and you'll get 8 servings that are 6 oz.

Divide 200 servings that are 6 oz. by 8 servings that are 6 oz. and you'll get 25.

1 one can + 3 cans of water= 4 oz, also we can set up a ratio using these numbers 1/3 .
12 ounce cans + x water = x 0z. Now we can find out how much water is needed.
1/3 x 12/x; x= 36, hence 12/36= 48 oz.

now we need to know 12 ounce cans of the concentration are required to prepare 200-6 ounce serving.
200- 6 ounce serving is equal to 1200oz, and we have a 48oz of unit can of 12 ounces. Divinding 1200 by 48 we get 25.
that's how many 12ounces cans we need.

C: number of cans
in every can there is 4c of concerate and water
thus 12*4c=200*6
after computation you find
c= 25.

this problem can be viewed in the following way.
you have 4 workers can accomplish a task in 12 days.
we 6 workers can accomplish a task in 200 days.
the question how many more days the 4 workers require to the accomplish the task of 6 workers.
4*12*a=6*200 (men days)
then you will get

a= 25.

1 serving = 4 cans = 1 concentrate + 3 water

You want 100 (12 oz)servings or 200 (6 oz) servings

So you need 100*1/4 = 25 cans