Jennifer has a recipe that calls for horseradish sauce that is 45% pure horseradish. At the grocery store she finds one horseradish sauce that is 30% pure horseradish and another that is 80% pure horseradish. How many teaspoons of each of these horseradish sauces should Jennifer mix together to get 4 teaspoons of horseradish sauce that is 45% pure horseradish?
Paula Scott, a massage therapist needs 3 ounces of a 20% lavender
oil solution. She has only 5% and 30% lavender oil solutions available.
How many ounces of each should Paula mix to obtain the desired
solution?
To solve this problem, we need to find the number of teaspoons of each horseradish sauce that Jennifer should mix together to get the desired 4 teaspoons of horseradish sauce that is 45% pure.
Let's assume Jennifer uses x teaspoons of the 30% pure horseradish sauce.
Then, she would be using (4 - x) teaspoons of the 80% pure horseradish sauce.
Now, let's calculate the amount of pure horseradish in each type of sauce:
For the 30% pure horseradish sauce, the amount of pure horseradish is 0.3 * x.
For the 80% pure horseradish sauce, the amount of pure horseradish is 0.8 * (4 - x).
Since we want the final mixture to be 4 teaspoons of horseradish sauce that is 45% pure, we can set up the following equation:
0.3x + 0.8(4 - x) = 0.45 * 4
Let's solve this equation to find the value of x:
0.3x + 3.2 - 0.8x = 1.8
Now, let's combine like terms:
-0.5x + 3.2 = 1.8
Next, let's isolate the variable by subtracting 3.2 from both sides:
-0.5x = -1.4
Then, we can solve for x by dividing both sides by -0.5:
x = -1.4 / -0.5
x = 2.8
Since the number of teaspoons cannot be negative, we discard this solution.
Therefore, there is no solution to this problem. Jennifer cannot mix the 30% and 80% horseradish sauces to obtain a 4-teaspoon mixture that is 45% pure horseradish.