I have 8 cups of a juice drink consisdting of 25% oj and 75% apple juice. I want to make a mix with 40% oj. how many cups of oj must I add?
Oj: x
Apple juice: (8-x)
.25x + .75(8-x) = .4(8)
.25x + 6 -.75x = 3.2
6 -0.5x = 3.2
-.5x = 3.2-6
-.5x = -2.8
x = 5.6
OJ
.5(8) + x = 2+x
Total
8 + x
so
2+x = .4(8+x)
2 + x = 3.2 + .4 x
.6 x = 1.2
x = 2
To find out how many cups of orange juice (OJ) you must add, we can use the concept of proportions.
Let's break down the problem:
1. In your initial mixture of 8 cups, you have 25% OJ and 75% apple juice. This means that 25% of 8 cups are OJ, or (25/100) * 8 = 2 cups of OJ.
2. You want to make a new mixture with a concentration of 40% OJ. Let's assume you will add x cups of OJ to achieve this.
3. After adding x cups of OJ to the 8 cups, the total volume of the mixture will be 8 + x cups.
4. In the final mixture, you want the proportion of OJ to be 40%. This means that 40% of the final mixture should be OJ, or (40/100) * (8 + x) = (2 + x) cups of OJ.
Now, we can set up an equation to solve for x:
(2 + x) = (40/100) * (8 + x)
Let's solve this equation:
2 + x = (40/100) * (8 + x)
2 + x = (2/5) * (8 + x)
2 + x = (2/5) * 8 + (2/5) * x
2 + x = 16/5 + (2/5) * x
2 + x - (2/5) * x = 16/5
(5/5)x + x - (2/5) * x = 16/5
(3/5)x = 16/5 - 10/5
(3/5)x = 6/5
To isolate x, we can multiply both sides of the equation by (5/3):
(5/3) * (3/5)x = (5/3) * (6/5)
x = 6/3
x = 2
Therefore, you must add 2 cups of orange juice to achieve a mixture with 40% OJ.