Problem Solving

According to the directions on a can of frozen orange juice concentrate,1 can of a concentrate is to be mxed 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
[spoiler]OA = A[/spoiler]

1 can concentrate = 4(=1+3) cans of juice
200*6 ounce servings of juice will require: (1/4)*200*6/12 = 25
IMO A

Why the answer is not [spoiler]E?[/spoiler]

My logic is like this :

x cans concentrate, 12-ounce servings of juice
100-x cans of water, 36-ounce cans of water (from the 1:3 ratio)
----------------------------------------------------------------

200 cans of 6-ounce orange juice which also means 100 cans of 12-ounce of juice

12x+36*(100-x)=12*100
X : 100

Where am I wrong?
Thank you in advance.

Ozlemg wrote:Why the answer is not [spoiler]E?[/spoiler]

My logic is like this :

x cans concentrate, 12-ounce servings of juice
100-x cans of water, 36-ounce cans of water (from the 1:3 ratio)
----------------------------------------------------------------

200 cans of 6-ounce orange juice which also means 100 cans of 12-ounce of juice

12x+36*(100-x)=12*100
X : 100

Where am I wrong?
Thank you in advance.

The line in red: we know 1 can concentrate + 3 cans water = 4 cans juice.
Thus its not (1:3) ratio. The ratio is 4:3.
i.e. for 4 cans juice, you have 3 cans water.
Thus, for 12 cans juice, you have 9 cans of water. (not 36)

Also the way i solved:
1 can concentrate makes 4 cans of juice.
Total juice needed = 200*6 = 1200 ounces.
Thus no. of concentrate ounces needed = 1200/4 = 300
Now, we need 300 ounces of concentrate. but each can is of 12 ounces.
Thus no. of cans needed = 300/12 = 25
Hope it's clear

first of all you are introducing different values for x -> 12-ounce and 36-ounce very strange of not wrong initially
secondly you must not equate the no-s of cans with water to the no-s of cans with juice, your second mistake after assigning different values for x

this q. is simple and combines ration conversion: a is to b means a/b, a is to both a&b is a/(a+b)
1/3, 1/(1+3) or 1/4
one can of concentrate is to four parts of juice
200 cans of cans of 6-ounce juice is 100 can of 12-ounce juice
and 1/4 with x/100 makes x=25

Ozlemg wrote:Why the answer is not [spoiler]E?[/spoiler]

My logic is like this :

x cans concentrate, 12-ounce servings of juice
100-x cans of water, 36-ounce cans of water (from the 1:3 ratio)
----------------------------------------------------------------

200 cans of 6-ounce orange juice which also means 100 cans of 12-ounce of juice

12x+36*(100-x)=12*100
X : 100

Where am I wrong?
Thank you in advance.

total = 200 * 6 = 1200

O: W = 1:3 means
O+w = 1200
4O = 1200
O = 300

number of 12 ounce Orange juices req = 300/12 = 25.

A it is.