Question

5. A type of green paint is made by mixing 2 cups of yellow with 3.5 cups

of blue. (Lesson 2-1)
a. Find a mixture that will make the same shade of green but a
smaller amount.
b. Find a mixture that will make the same shade of green but a
larger amount.
c. Find a mixture that will make a different shade of green that is bluer.
d. Find a mixture that will make a different shade of green that is
more yellow.

Answer 1

To create different amounts and shades of green paint, maintain or adjust the ratio of yellow to blue. A smaller or larger batch can be made by scaling the 2:3.5 ratio of yellow to blue. Different shades are achieved by altering the ratio to have more blue or more yellow.

Step-by-step explanation:

The question involves finding different mixtures of paint to achieve various shades of green. The original paint mixture is made by combining 2 cups of yellow with 3.5 cups of blue. We can use ratios to solve the problems:

1. a. Smaller amount: To maintain the same shade of green but with a smaller total amount, we keep the ratio of yellow to blue the same. This is a ratio of 2:3.5, which can also be written as 4:7. So, to make a smaller batch, we could mix 4 tsp of yellow with 7 tsp of blue.
2. b. Larger amount: Similarly, for a larger amount with the same shade, we scale up the mixture while maintaining the 2:3.5 ratio. For example, doubling the original would mean mixing 4 cups of yellow with 7 cups of blue.
3. c. Bluer shade: To make a different shade of green that is bluer, we need to increase the amount of blue relative to yellow. For example, we could mix 2 cups of yellow with 5 cups of blue.
4. d. More yellow: Conversely, to make the green shade more yellow, we would decrease the amount of blue relative to yellow. An example mixture could be 3 cups of yellow with 3.5 cups of blue.

By manipulating the ratios of yellow to blue paint, we can create varying amounts and shades of green paint.