"(purple smooth = 75, white smooth = 28, purple wrinkled = 24, white wrinkled = 8) which alleles are dominant? "

The alleles which cause the color to be purple and appearance to be smooth are dominant.

This is a typical case of Mendelian dihybrid cross in which the ratio of the off-springs is 9:3:3:1 and the off-springs with highest output i.e. 9 are generated out of dominant alleles. So if we will compare the results mentioned in the question we can easily infer that these off-springs also have similar ratio as described above.

Explanation:

purple smooth = 75

white smooth = 28

purple wrinkled = 24

white wrinkled = 8

If we will divide purple smooth = 75 by 8 which is the output of white wrinkled, we will get 9.4 as answer which is ~9.

If we will divide white smooth = 28 by 8 which is the output of white wrinkled, we will get 3.5 as answer which is ~3.

If we will divide purple wrinkled = 24 by 8 which is the output of white wrinkled, we will get 3 as answer.

Hence, the ratio of purple smooth : white smooth : purple wrinkled : white wrinkled = 9:3:3:1.

The purple smooth allele

Explanation:

This is obviously due to the high phenotypic ratio of the allele plus its has the highest visible number