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.

A proportional relationship is written as:

y = k*x

Where k is the constant of proportionality.

Here we have a proportional relationship between yellow paint and blue paint to make a particular shade of green.

We will see that we need 5 cups of yellow paint to get this particular shade of green.

In the table, we can see that if we mix 2 cups of blue paint and 10 cups of yellow paint we get that shade of green.

Let's define:

Replacing that in the general proportional relation we get:

10 = k*2

With this we can find the value of k:

10/2 = 5 = k

k = 5

Then the proportional relation is: y = 5*x

Now we want to see how many cups of yellow paint we need to mix with one cup of blue paint to get this particular shade of green, then we just need to replace x by 1.

y = 5*1 = 5

This means that we need 5 cups of yellow paint.

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From the given table we can see that mixture of 2 cups of blue paint and 10 cups of yellow paint produced green cups.

So , the ratio of yellow to blue is , .

We need to find , the number of cups of yellow paint should we mix with 1 cup of blue paint to make the same shade of green.

We know , produce same shade ratio should be constant.

Let , cups of yellow shade is x .

Therefore , cups of yellow shades required are 5.

Hence, this is the required solution.

ab will be equal to