Final answer:
To make a larger amount of the same shade of green paint, one must maintain the original ratio of yellow to blue, which is 2:3.5 or 4:7. So, for a mixture that is 'n' times larger, use 2n cups of yellow and 3.5n cups of blue.
Step-by-step explanation:
The question involves finding a proportionate mixture of two colors to make a specific shade of green. In the given mix, 2 cups of yellow are combined with 3.5 cups of blue. To make a larger amount with the same shade, we must keep the ratio of yellow to blue the same, which is 2:3.5 or simplified to 4:7.
Let's find a larger mixture amount that maintains this ratio. If we doubled the initial quantities, we would use 4 cups of yellow and 7 cups of blue. However, any multiple of these quantities would work. For example, if we triple the original mix, we would use 6 cups of yellow (2 cups × 3) and 10.5 cups of blue (3.5 cups × 3). The critical point is that the ratio of yellow to blue remains consistent.
To generalize, if we want to make a mixture that is n times larger, we would use 2n cups of yellow and 3.5n cups of blue, thereby keeping the mixture proportions the same and resulting in the same shade of green.