Question

To make a certain shade of green, Kyle mixes 2 cups of blue paint with 10 cups of yellow paint. If he needs to make more green paint but only has 1 cup of blue left, he will need 5 cups cups of yellow paint.What is a proportional relationship represented in the problem?what is the constant of proportionality for problem 1 what does it represent

Answer 1

To make the green paint, kyle uses:

2 cups of blue paint for 10 cups of yellow paint

He has 1 cup of blue paint left to make more green, he will need 5 more cups of yellow paint.

This means that for 3 cups of blue paint, he will need 15 cups of yellow paint.

Cups of blue paint = 2 + 1 = 3

Cups of yellow paint = 10 + 5 = 15

Thus, we have the table:

Cups of blue paint(x) Cups of yellow paint(y)

1 5

2 10

3 15

a) The proportional relationship represented in the problem is a direct proportion.

We can say that the cups of yellow paint is directly proportional to the cups of blue paint.

It is represented by:

y = kx

Where k is the constant of proportionality

To find the constant of proportionality, take any point on the table and solve for k.

Take the second points:

10 = 2k

Divide both sides by 2:

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

The constant of proportionality is 5

ANSWER:

a) Direct Proportion

b) Constant of proportionality = 5