I'm sorry but I'm confused about the steps you took in the part of the equation that you began to solve for me.
Maria has 8 cups of a fruit punch that consists of 25% orange juice and 75% apple juice. She wants to make a drink that is 40% orange juice. How many cups of orange juice should Maria add to the mixture?
A: ?
Sorry I misread your original question
So here is the correct one:
right now :
amount of orange juice = .25(8) = 2 cups
amount of apple juice = .75(8) = 6 cups
let the amount of pure orange juice to be added be x cups
so just looking at the orange juice:
2 + x = .4(x+8)
times 10
20 + 10x = 4x + 32
6x = 12
x = 2
She should add 2 cups of pure orange juice
check:
She now has 10 cups of juice, which contains the original 2 cups of orange juice from the original mixture plus the 2 cups of pure orange juice
So it contains 4 cups of orange juice or 4/10 or 40% orange juice.
Thank you so much!
To solve this problem, we need to find out how many cups of pure orange juice Maria needs to add to the existing mixture in order to achieve a 40% concentration. Here are the steps:
Step 1: Calculate the total amount of juice in the existing mixture.
Since Maria has 8 cups of fruit punch, and it consists of 25% orange juice and 75% apple juice, we can calculate the amount of orange juice in the mixture as follows:
8 cups * 0.25 (25%) = 2 cups of orange juice.
Step 2: Determine the amount of orange juice needed to achieve a 40% concentration.
Let's assume Maria needs to add x cups of pure orange juice. Since the desired concentration is 40%, we can calculate the amount of orange juice in the mixture after adding x cups as follows:
(2 cups + x cups) * 0.4 (40%) = 0.4x + 0.8 cups of orange juice.
Step 3: Set up an equation to solve for x.
Since we want the amount of orange juice in the mixture to be equal to 0.4x + 0.8 cups, we can set up the equation:
0.4x + 0.8 = x
Step 4: Solve the equation.
To solve the equation, we will isolate the variable x by subtracting 0.4x from both sides of the equation:
0.4x + 0.8 - 0.4x = x - 0.4x
0.8 = 0.6x
Next, divide both sides of the equation by 0.6:
0.8/0.6 = x
1.3333... = x
Step 5: Round the final answer.
Since we can't have a fraction of a cup, round the solution to the nearest whole number. In this case, Maria should add approximately 1 cup of pure orange juice to the mixture in order to achieve a 40% concentration.
Thus, the answer is Maria should add 1 cup of orange juice to the mixture.