Sam Squeeze has 10 quarts of a drink that is 60% organge juice. how much pure orange juice must he add to get a drink that is 75% orange juice?
To find out how much pure orange juice Sam needs to add, we can set up an equation based on the given information.
Let x be the amount of pure orange juice Sam needs to add.
The amount of orange juice in the initial drink is 10 quarts * 60% = 6 quarts.
After adding x quarts of pure orange juice, Sam will have a total of 10 + x quarts of the final drink.
The amount of orange juice in the final drink will be 6 quarts + x quarts.
According to the equation, the percentage of orange juice in the final drink should be 75%.
So, we can set up the equation as follows:
(6 + x) / (10 + x) = 75 / 100
To solve this equation step by step:
1. Cross-multiply:
(6 + x) * 100 = 75 * (10 + x)
2. Distribute:
600 + 100x = 750 + 75x
3. Subtract 75x from both sides:
25x = 150
4. Divide both sides by 25:
x = 6
Therefore, Sam needs to add 6 quarts of pure orange juice to get a drink that is 75% orange juice.
To solve this problem, we need to determine how much pure orange juice Sam Squeeze must add to the 10 quarts of 60% orange juice drink to obtain a 75% orange juice drink.
Let's break down the problem into the following steps:
Step 1: Determine the amount of orange juice in the original drink
Since Sam has 10 quarts of a drink that is 60% orange juice, the amount of orange juice in that drink can be calculated by multiplying the total volume by the percentage of orange juice:
Orange juice in original drink = 10 quarts × 0.60 = 6 quarts
Step 2: Set up the equation
Let's assume Sam needs to add x quarts of pure orange juice to obtain the desired 75% orange juice drink.
The equation can be set up as follows:
Orange juice in original drink + Orange juice added = Orange juice in final drink
Substituting the values we have:
6 quarts + x quarts = (10 + x quarts) × 0.75
Step 3: Solve the equation
Simplifying the equation, we have:
6 + x = 0.75(10 + x)
6 + x = 7.5 + 0.75x
Subtracting 0.75x from both sides:
0.25x = 1.5
Dividing both sides by 0.25:
x = 6
Step 4: Answer the question
Sam needs to add 6 quarts of pure orange juice to the original 10 quarts of 60% orange juice drink to obtain a drink that is 75% orange juice.
At the start there must be 6Q orange and 4Q water.
Let the total final volume =V
and the volume of orange added =v
so at the end
10Q+v=V..........1
and
(6Q+v)/V=0.75 or
6Q+v=0.75V.......2
solve the two equations (1 and 2) to find v