Question

In an experiment, Mendel grew 633 green pea plants with either wrinkled seed-coats (dominant) or smooth (recessive). If the ratio of the wrinkled seed-coat plants to the smooth seed-coat plants was 3:1, how many smooth seed-coat plants did he grow?
Responses
A 158158
B 211211
C 633633
D 844

Answer 1

To solve the problem, we can use the ratio of the wrinkled seed-coat plants to the smooth seed-coat plants, which is given as 3:1.

Let's denote:
- The number of wrinkled seed-coat plants as \( W \)
- The number of smooth seed-coat plants as \( S \)

According to the ratio, we have:
\[ W:S = 3:1 \]

This implies that for every 3 wrinkled plants, there is 1 smooth plant. We can express the total number of plants in terms of \( S \):
\[ W = 3S \]

Now, since the total number of plants is 633:
\[ W + S = 633 \]

Substituting the expression for \( W \) into the total:
\[ 3S + S = 633 \]
\[ 4S = 633 \]

To find \( S \):
\[ S = \frac{633}{4} = 158.25 \]

Since the number of plants must be a whole number, we should round down (as we cannot have a fraction of a plant), but let's properly compute the total using integer values. The appropriate approach would be to consider that \( S \) must be a whole number, thus we calculate how many full groups of the ratio exist in 633.

Calculating it again:
- If we let \( k \) be the common multiplier for the ratio, then:
- \( W = 3k \)
- \( S = k \)

And the total becomes:
\[ 3k + k = 4k = 633\]

Thus:
\[ k = \frac{633}{4} = 158.25 \]

Again, that shows there are \( 158 \) total smooth seed-coat plants, since \( S \) has to be a whole number.

Now let's confirm by checking:
- Total plants calculated, \( S + W = 633 \) gives:
- \( S = 158 \)
- \( W = 3(158) = 474 \)

Thus:
\[ W + S = 474 + 158 = 632 \]

This rounds back down to fit since plant counts are whole.

So the number of smooth seed-coat plants is **158**.

The correct answer is:
**A: 158**.