Question

When you mix two colors of paint in equivalent ratios, the resulting color is always the same. Complete the table as you answer the questions. Cups of 1) How many cups of yellow paint should you mix with 1 cup of blue paint to make the same shade of green? Explain or show your reasoning. blue Cups of yellow paint paint 2 10 219 1 2 2) Make up a new pair of numbers that would make the same shade of green. Explain how you know they would make the same shade of green. 3) What kind of relationship is represented by this table? 4) What is the constant of proportionality? What does it represent?

Answer 1

To obtain the same shade of green, the ratio between the cups of yellow paint and blue paint must be always the same.

1)

To determine how many cups of yellow paint should be mixed with one cup of blue, you can use cross multiplication:

2 cups blue → 10 cups of yellow

1 cup of blue → x cups of yellow

Both relationships are at the same ratio so that:

`\begin{gathered} (10)/(2)=(x)/(1) \\ 5=x \end{gathered}`

For 1 cup of blue paint, you need to use 5 cups of yellow paint to mix the same shade of green.

This means that the blue-yellow paint ratio for this particular shade of green is 1:5, which means that for every cup of blue paint you add, you have to add 5 cups of yellow paint.

2)

Let's select 3 cups of blue paint. If for every cup of blue paint you need to add 5 cups of yellow paint, then to determine how many cups of yellow you need for 3 cups of blue paint, multiply the number of cups of blue paint by the number of yellow cups per cup of blue paint:

`3\cdot5=15`

So, if you use 3 cups of blue paint, you'll need 15 cups of yellow paint:

3) The relationship between the amount of blue and yellow paint needed is a direct relationship since both variables increase and decrease together.

4) The constant of proportionality is k=5 → it represents the increase in the number of yellow paint cups every time another cup of blue paint is added.