Cranberry juice costs $6.30 per quart and apple juice costs $3.60 per quart.  Terrence wants to make a mixture of apple and cranberry juice that sells for$4.50 per quart. How many quarts q of cranberry juice should he mix with 4 quarts of apple juice to make cranberry-apple juice at that price? Which equation below represents the situation?

To solve this, let's use a weighted average approach.

We want to mix cranberry juice, which costs $6.30 per quart, with apple juice, which costs $3.60 per quart, to make a mixture that costs $4.50 per quart. The number of quarts of cranberry juice is $ q $, and Terrence is using 4 quarts of apple juice.

The total cost of the mixture can be expressed as the weighted average of the costs:

\[
\frac{6.30q + 3.60 \times 4}{q + 4} = 4.50
\]

Now, let's break it down:

- $ 6.30q $ is the cost of $ q $ quarts of cranberry juice.
- $ 3.60 \times 4 $ is the cost of 4 quarts of apple juice.
- The total number of quarts is $ q + 4 $.
- We want the mixture to sell for $4.50 per quart.

Thus, the equation representing the situation is:

\[
\frac{6.30q + 3.60 \times 4}{q + 4} = 4.50
\]

Would you like to see the step-by-step process of solving this equation?

Here are 5 related questions:
1. How do you solve weighted average problems in general?
2. What is the solution for $ q $ in this specific problem?
3. How would this change if the desired price was $5 per quart?
4. Can you write a similar problem but with different prices?
5. How do you check the solution once you find $ q $?

**Tip:** When solving problems involving mixtures, it's important to set up the equation based on the total cost and total quantity.

Cranberry juice costs $6.30 per quart and apple juice costs $3.60 per quart. Terrence wants to make a mixture of apple and cranberry juice that sells for $4.50 per quart. How many quarts q of cranberry juice should he mix with 4 quarts of apple juice to make cranberry-apple juice at that price? Which equation below represents the situation?

Discover how to solve a weighted average problem involving cranberry juice at $6.30 per quart and apple juice at $3.60 per quart to create a mixture priced at $4.50 per quart. This algebraic problem is perfect for high school students in Grades 9-12 and covers the application of linear equations and weighted averages.

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