If there are 7 white t-shirts on the shelf for every 3 purple shirts, we can use this ratio to determine the number of white shirts if there are a total of 40 purple and white shirts.
To find the number of white shirts, we need to divide the total number of shirts by the sum of the parts in the ratio (7 + 3 = 10), and then multiply that result by the number of parts representing white shirts (7).
So, for every 10 shirts, 7 of them are white.
If there are a total of 40 purple and white shirts, we can set up a proportion:
7 white shirts / 10 total shirts = x white shirts / 40 total shirts.
To solve for x, we cross-multiply and solve the equation:
7 * 40 = 10 * x
280 = 10 * x
280 / 10 = x
28 = x
Therefore, there are 28 white shirts among the 40 purple and white shirts.