Question

1. the table shows the relationship between the different colors needed to make a shade of purple paint and the total amount of paint. write a part - to - part and a part - to - whole ratio that represents the relationship in the table. then use the ratios to find the unknown values. (example 3)

blue (fl oz)	10	15		25
total paint (fl oz)	16		32	40

Explanation:

Step1: Find the ratio of Blue to Red (part - to - part)

From the first row, Blue = 10 fl oz and Red = 6 fl oz. So the ratio of Blue to Red is $\frac{10}{6}=\frac{5}{3}$. Also, the ratio of Red to Blue is $\frac{6}{10}=\frac{3}{5}$. The total paint is Blue + Red, so 10 + 6 = 16 fl oz, which matches the first total.

Step2: Find the ratio of Blue to Total (part - to - whole)

Blue = 10, Total = 16, so the ratio of Blue to Total is $\frac{10}{16}=\frac{5}{8}$. The ratio of Red to Total is $\frac{6}{16}=\frac{3}{8}$.

Step3: Calculate the second row (Blue = 15)

Sub - step 3.1: Find Red when Blue = 15 (using Blue to Red ratio $\frac{5}{3}$)

Let Red be $x$. Then $\frac{15}{x}=\frac{5}{3}$. Cross - multiply: $5x = 15\times3\Rightarrow5x = 45\Rightarrow x = 9$.

Sub - step 3.2: Find Total when Blue = 15 and Red = 9

Total = 15 + 9 = 24.

Step4: Calculate the third row (Total = 32)

Sub - step 4.1: Find Blue when Total = 32 (using Blue to Total ratio $\frac{5}{8}$)

Let Blue be $y$. Then $\frac{y}{32}=\frac{5}{8}$. Cross - multiply: $8y=32\times5\Rightarrow8y = 160\Rightarrow y = 20$.

Sub - step 4.2: Find Red when Total = 32 and Blue = 20

Red = 32 - 20 = 12.

Step5: Calculate the fourth row (Blue = 25)

Sub - step 5.1: Find Red when Blue = 25 (using Blue to Red ratio $\frac{5}{3}$)

Let Red be $z$. Then $\frac{25}{z}=\frac{5}{3}$. Cross - multiply: $5z = 25\times3\Rightarrow5z = 75\Rightarrow z = 15$.

Sub - step 5.2: Verify with Total (Blue + Red)

Total = 25+15 = 40, which matches the given total.

Answer:

• Part - to - part ratio (Blue to Red): $\boldsymbol{\frac{5}{3}}$ (or Red to Blue: $\boldsymbol{\frac{3}{5}}$)
• Part - to - whole ratio (Blue to Total): $\boldsymbol{\frac{5}{8}}$ (or Red to Total: $\boldsymbol{\frac{3}{8}}$)

Filled Table:

Blue (fl oz)	10	15	20	25
Total Paint (fl oz)	16	24	32	40