Kinda stuck on this genetics question. Help please?

In sweet peas, genes C and P are necessary for colored flowers. In the absence of either (__pp or cc__), or both (cc, pp), the flowers are white. Give the probable genotype of a plant with colored flowers and a plant with white flowers that produced 38 plants with colored flowers and 42 with white flowers.
Kinda stuck on this genetics question. Help please?
When trying to solve a problem like this, it helps to look at the ratio of the offspring. Ratios generally are in 3:1, 1:2:1, or 1:1 relationships. Given that your "results" are 38 and 42, this is closest to 1:1.



It would be easier for you to see how to do this if you only had one gene to follow. Consider that when you cross a red flower (RR) with a white one (rr).



If the trait was completely dominant (RR and Rr = red, rr = white. Try some test crosses:



Rr x Rr



__R___r

R| RR | Rr (a 3red:1white result)

r | Rr | rr





RR x rr

__R___R

r| Rr | Rr (all alike, or 1 type produced)

r| Rr | Rr



Rr x rr

__R___r

r| Rr | rr (a 1red:1white ratio)

r| Rr | rr



That should immediately eliminate two heterozygous parents, because that would give you a 3:1 ratio and one homozygous dominant and one homozygous recessive. So the key is to have one heterozygous and one homozygous recessive.



Now to confuse things by throwing in the second gene!



If I understand your problem having either the C or P being recessive, or if both are recessive you get a white flower. Look at the different possibilities:



CcPp x ccpp

The first parent can produce gametes of CP, Cp, cP, and cp

The second can only produce cp.

The results would be CcPp (colored) Ccpp (white) ccPp (white) and ccpp (white) - a 3:1 ratio, so that doesn't work.



CcPP x ccpp

Now the first parent can produce CP or cP, the second cp.

The results would be CcPp (colored) or ccPp (white, because of the cc) - you get one colored to 1 white.



Is that the only answer?



CCPp x ccpp

Now the first parent can produce CP or Cp, the second cp.

The results would be CcPp (colored) or Ccpp (white, because of the pp) - you get one colored to 1 white.



Another way to look at this is by multiplying the ratios. The first croos I did with the two traits (CcPp x ccpp) would have ratios of 1/2 (for the c by itself) and 1/2 (for the p by itself). When you multiply 1/2 x 1/2 you get 1/4 (or one out of four, or 3:1). The second cross had a ratio of 1/2 for the c and 1 for the p, so 1/2 x 1 = 1/2 which is what you want. The third cross had ratios of 1 for the c and 1/2 for the p, so 1 x 1/2 = 1/2.



If you know the 3 ratios for the single crosses, just figure out which you need to multiply together to get the ratio you want, and that will let you know what genotypes are needed (and remember, there can be more than one way to get the result you want).



Note: This only works the way I've shown you if the trait isn't sex-linked. The 1:2:1 only occurs if the trait is codominant or incompletely dominant - that is a Rr flower would be striped or spotted (both possibilities for codominant), or pink (incomplete dominance).
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