Question

10 0/2 points fill in the blank you mix \\(\frac{2}{3}\\) quart of blue paint for every \\(\frac{1}{4}\\) quart of red paint. you want to make a total of \\(5\frac{1}{2}\\) quarts of purple paint. in order to make \\(5\frac{1}{2}\\) quarts of purple paint, how much blue paint and how much red paint do you need to use? 122 quarts of blue paint 2/3 quarts of red paint

Explanation:

Step1: Find paint ratio sum

First, calculate the total amount of paint in one base mixture by adding the blue and red portions.
$\frac{2}{3} + \frac{1}{4} = \frac{8}{12} + \frac{3}{12} = \frac{11}{12}$ quarts

Step2: Calculate number of batches

Divide the total desired paint by the base mixture size to find how many full batches are needed. Convert $5\frac{1}{2}$ to an improper fraction first: $5\frac{1}{2} = \frac{11}{2}$.
$\frac{11}{2} \div \frac{11}{12} = \frac{11}{2} \times \frac{12}{11} = 6$ batches

Step3: Compute blue paint amount

Multiply the blue paint per batch by the number of batches.
$6 \times \frac{2}{3} = 4$ quarts

Step4: Compute red paint amount

Multiply the red paint per batch by the number of batches.
$6 \times \frac{1}{4} = \frac{6}{4} = \frac{3}{2} = 1\frac{1}{2}$ quarts

Answer:

4 quarts of blue paint
$1\frac{1}{2}$ (or $\frac{3}{2}$) quarts of red paint