Question
6. Andre makes green paint by mixing 5 cups of yellow paint with 2 cups of blue paint. a. To make the same shade of green, how much yellow paint does Andre need if he uses 8 cups of blue paint?
Ask by John Reed. in the United States
Jan 30,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
Andre needs 20 cups of yellow paint when using 8 cups of blue paint.
Solution
To maintain the same shade of green, Andre needs to keep the ratio of yellow paint to blue paint consistent. Originally, the ratio is:
\[ \frac{\text{Yellow}}{\text{Blue}} = \frac{5}{2} \]
If Andre uses 8 cups of blue paint, we can set up the proportion to find the required amount of yellow paint (\( y \)):
\[ \frac{y}{8} = \frac{5}{2} \]
To solve for \( y \):
\[ y = \frac{5}{2} \times 8 \]
\[ y = 5 \times 4 \]
\[ y = 20 \]
**Answer:** Andre needs **20 cups** of yellow paint when using 8 cups of blue paint.
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Simplify this solution Mind Expander
To maintain the same shade of green, we can use a ratio based on Andre's original recipe. In the original mix, the ratio of yellow to blue is 5:2. If Andre uses 8 cups of blue paint, he can set up a proportion to find the required amount of yellow paint: \( \frac{5}{2} = \frac{x}{8} \), where \( x \) is the amount of yellow needed. Solving for \( x \) gives Andre 20 cups of yellow paint. So, for 8 cups of blue paint, Andre would need 20 cups of yellow to achieve that same shade of green! Mixing it just right is like a painter's secret—keep those colors harmonious!
