In a unique species of plants, flowers may be yellow, blue, red, or mauve. All colors may be true-breeding. If plants with blue flowers are crossed to red-flowered plants, all F1 plants have yellow flowers. When these produced an F2 generation, the following ratio was observed: 9/16 yellow, 3/16 blue, 3/16 red, and 1/16 mauve. Determine the F1 results of a cross between true-breeding red and true-breeding mauve flowered plants.

flowers may be yellow, blue, red, or mauve
colors may be true-breeding
the cross of blue-flowered plants with red-flowered plants, produce plants that have yellow flowers
F2 generation: 9/16 yellow, 3/16 blue, 3/16 red, and 1/16 mauve.

Knowing that the phenotypic ratio is 9:3:3:1, we can assume that there are two genes involved in the flower color expression. We can name these genes B and R with a dominant and a recessive allele each (B, b and R, r respectively).

According to the first cross, we might establish the following genotypes:

1st Cross: blue-flowered plant x red-flowered plant

Parentals) BBrr x bbRR

Gametes) Br, Br, Br, Br bR, bR, bR, bR

F1) 100% BbRr, yellow plants

Parentals) BbRr x BbRr

Gametes) BR, Br, bR, br

BR, Br, bR, br

Punnett square) BR Br bR br

BR BBRR BBRr BbRR BbRr

Br BBRr BBrr BbRr Bbrr

bR BbRR BbRr bbRR bbRr

br BbRr Bbrr bbRr bbrr

F2) 9/16 yellow ---> 1/16 BBRR + 2/16 BBRr + 4/16 BbRr + 2/16 BbRR

3/16 blue ------> 1/16 BBrr + 2/16 Bbrr

3/16 red---------> 1/16 bbRR + 2/16 bbRr

1/16 mauve ----> 1/16 bbrr

So,

Yellow-flowered plants: BBRR, BBRr, BbRR, BbRr
Red-flowered plants: bbRR, bbRr
Blue-flowered plants: BBrr, Bbrr
Mauve-flowered plants: bbrr

According to these genotypes, the second cross would be like following,

2nd Cross: true-breeding red-flowered plants with true-breeding mauve flowered plants.

Parentals) bbRR x bbrr

Phenotype) Red Mauve

Gametes) bR, bR, bR, bR br, br, br, br

Punnett square) bR bR bR bR

br bbRr bbRr bbRr bbRr

F1) 100% bbRr, red flowered plants.