Question

1. a green paint mixture uses 5 cups of yellow paint for every 4 cups of blue paint. the table shows different quantities of yellow and blue paint for the same shade of green. complete the table.

yellow paint (cups)	blue paint (cups)
	1
1
	5
6

Explanation:

The ratio of yellow paint to blue paint is \( 5:4 \), which means the relationship between yellow paint (\( y \)) and blue paint (\( b \)) can be represented by the proportion \( \frac{y}{b}=\frac{5}{4} \), or \( y = \frac{5}{4}b \) and \( b=\frac{4}{5}y \). We will use these formulas to find the missing values.

Step 1: Find yellow paint when blue paint is 1 cup

We know the ratio \( \frac{y}{b}=\frac{5}{4} \). Substitute \( b = 1 \) into the formula \( y=\frac{5}{4}b \).
\( y=\frac{5}{4}\times1=\frac{5}{4} = 1.25 \)

Step 2: Find blue paint when yellow paint is 1 cup

Using the formula \( b=\frac{4}{5}y \), substitute \( y = 1 \).
\( b=\frac{4}{5}\times1=\frac{4}{5}=0.8 \)

Step 3: Find yellow paint when blue paint is 5 cups

Using the formula \( y=\frac{5}{4}b \), substitute \( b = 5 \).
\( y=\frac{5}{4}\times5=\frac{25}{4} = 6.25 \)

Step 4: Find blue paint when yellow paint is 6 cups

Using the formula \( b=\frac{4}{5}y \), substitute \( y = 6 \).
\( b=\frac{4}{5}\times6=\frac{24}{5}=4.8 \)

Now we can complete the table:

yellow paint (cups)	blue paint (cups)
\( \frac{5}{4} \) (or 1.25)	1
1	\( \frac{4}{5} \) (or 0.8)
\( \frac{25}{4} \) (or 6.25)	5
6	\( \frac{24}{5} \) (or 4.8)

Answer:

The completed table (filling in the missing values) is as above. The missing values are \( 1.25 \) (for yellow when blue is 1), \( 0.8 \) (for blue when yellow is 1), \( 6.25 \) (for yellow when blue is 5), and \( 4.8 \) (for blue when yellow is 6).