Final answer:
To find the number of batches made with 15 cups of red paint when there is a ratio of 3 red paints to 2 blue paints, you can set up a proportion and solve for the unknown variable.
Step-by-step explanation:
To find the number of batches made with 15 cups of red paint, we need to set up a proportion using the information given. We know that there are 3 red paints to 2 blue paints. So the ratio of red paints to total paints is 3:5. Let's represent the number of batches as x:
3 red paints / 5 total paints = 15 red paints / x total paints
To determine how many batches of paint can be made with 15 cups of red paint using a ratio of 3 red paints to 2 blue paints, we can set up a proportion. The problem indicates that 3 cups of red paint are used for each batch. If we want to make batches with 15 cups of red paint, we divide 15 cups by the 3 cups used per batch:
15 cups red paint ÷ 3 cups per batch = 5 batches
Therefore, 5 batches can be made with 15 cups of red paint. Next, we find the number of blue cups needed for those 5 batches using the ratio:
5 batches × 2 blue cups per batch = 10 blue cups
To solve for x, we can cross-multiply:
3x = 15 x 5
3x = 75
x = 25
Therefore, 25 batches can be made with 15 cups of red paint.