A certain shade of green paint is made of 6 quarts of blue paint for every 5 quarts of yellow paint. If you only have 1 quart of blue paint, how much yellow paint should you use to make the same shade of green paint?

Question

Start by setting up a table that could be used to find the amount of yellow paint you need for every 1 quart of blue paint.
Blue Paint (qt) Yellow Paint (qt)

1

?

6

5
Nice!
You’re trying to find the amount of yellow paint you would need for every 1 quart of blue paint. What do you need to divide 6 quarts of blue paint by to find 1 quart of blue paint?
÷
6
Blue Paint (qt) Yellow Paint (qt)
6 5
1 ?
Good work!
You need to divide 6 quarts of blue paint by 6 to find 1 quart of blue paint. To keep the ratio the same, you also need to divide 5 quarts of yellow paint by 6. What is 5 ÷ 6?
÷ 6
÷ 6
Blue Paint (qt) Yellow Paint (qt)
6 5
1

Answer 1

To find out how much yellow paint you should use for 1 quart of blue paint while maintaining the same ratio, you can divide the amount of yellow paint by the same factor you used to determine the amount of blue paint.

You have the original ratio of blue paint to yellow paint as 6 quarts of blue to 5 quarts of yellow.

To find the amount of yellow paint corresponding to 1 quart of blue paint, you can set up the calculation like this:

\[ \text{Amount of yellow paint} = \frac{\text{Original amount of yellow paint}}{\text{Original amount of blue paint}} \times \text{Amount of blue paint you have} \]

This becomes:

\[ \text{Amount of yellow paint} = \frac{5 \text{ quarts}}{6 \text{ quarts}} \times 1 \text{ quart} \]

Now, performing the division:

\[ 5 ÷ 6 = \frac{5}{6} \text{ quarts} \]

So, for every 1 quart of blue paint, you would need \(\frac{5}{6}\) quarts of yellow paint.

Here's the completed table:

\[ \begin{array}{|c|c|} \hline \text{Blue Paint (qt)} & \text{Yellow Paint (qt)} \ \hline 1 & \frac{5}{6} \ 6 & 5 \ \hline \end{array} \]

Thus, you should use \(\frac{5}{6}\) quarts of yellow paint to make the same shade of green paint with 1 quart of blue paint.