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)

Answer 1

To find the amount of yellow paint needed for every 1 quart of blue paint based on the original ratio of blue to yellow (6 quarts of blue for every 5 quarts of yellow), we can set up a table using the given ratio.

First, we can determine the ratio of yellow paint to blue paint:

\[ \text{Ratio of Yellow to Blue} = \frac{5 \text{ quarts of yellow}}{6 \text{ quarts of blue}} \]

Now we can find how much yellow paint is needed when you have 1 quart of blue paint. To do this, you can set a proportion based on the ratio:

\[ \frac{5 \text{ qt yellow}}{6 \text{ qt blue}} = \frac{y \text{ qt yellow}}{1 \text{ qt blue}} \]

Cross-multiplying gives us:

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

Now we can set up the table:

| Blue Paint (qt) | Yellow Paint (qt) | |------------------|--------------------| | 1 | \(\frac{5}{6}\) | | 2 | \(\frac{5}{3}\) | | 3 | 2 | | 4 | \(\frac{20}{6}\) or \(\frac{10}{3}\) | | 5 | \(\frac{25}{6}\) | | 6 | 5 |

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