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.

F1) 100% bbRr, red flowered plants.

Explanation:

Available data:

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,

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

                    br    bbRr     bbRr    bbRr     bbRr

                    br    bbRr     bbRr    bbRr     bbRr

                    br    bbRr     bbRr    bbRr     bbRr

F1) 100% bbRr, red flowered plants.

the question isn't complete here so i can't right an answer '_'