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	20	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 $10:6=\frac{10}{6}=\frac{5}{3}$. Also, the ratio of Red to Blue is $6:10 = \frac{3}{5}$.
The part - to - whole ratio: For Blue to Total, it is $10:16=\frac{10}{16}=\frac{5}{8}$. For Red to Total, it is $6:16=\frac{6}{16}=\frac{3}{8}$.

Step2: Find the unknown for Red when Blue = 15

Let the amount of Red be $x$. Since the ratio of Blue to Red is $5:3$ (from $10:6$), we have $\frac{15}{x}=\frac{5}{3}$. Cross - multiplying gives $5x = 15\times3=45$, so $x = 9$. The total paint here is $15 + 9=24$ fl oz.

Step3: Find the unknown for Blue when Total = 32

Let the amount of Blue be $y$. Since the ratio of Blue to Total is $\frac{5}{8}$, we have $\frac{y}{32}=\frac{5}{8}$. Cross - multiplying gives $8y=32\times5 = 160$, so $y = 20$. Then the amount of Red is $32 - 20 = 12$ fl oz.

Step4: Find the unknown for Red when Blue = 25

Let the amount of Red be $z$. Since the ratio of Blue to Red is $\frac{5}{3}$, we have $\frac{25}{z}=\frac{5}{3}$. Cross - multiplying gives $5z=25\times3 = 75$, so $z = 15$. We can also check with total paint: $25+15 = 40$ fl oz (which matches the given total).

Answer:

• Part - to - part ratio (Blue to Red): $10:6$ (or simplified $5:3$); Part - to - whole ratio (Blue to Total): $10:16$ (or simplified $5:8$)
• Unknown values:
• When Blue = 15 fl oz, Red = 9 fl oz, Total = 24 fl oz.
• When Total = 32 fl oz, Blue = 20 fl oz, Red = 12 fl oz.
• When Blue = 25 fl oz, Red = 15 fl oz.