What number should replace the letter [tex]$x$[/tex] in the 'Seed color' row?
| Plant height | 787 tall | 277 short |
|---|---|---|
| Flower color | 705 purple | 224 white |
| Pod color | 428 green | 152 yellow |
| Pod shape | 882 inflated | 299 constricted |
| Seed color | 6,022 yellow | x green |
| Seed shape | 5,474 smooth | 1,850 wrinkled |
A. 18,066
B. 3,011
C. 207
D. 2,001
Answer (2)
Assume a 3:1 ratio of yellow to green seeds.
Set up the equation x 6022 = 1 3 .
Solve for x : x = 3 6022 ≈ 2007.33 .
Choose the closest integer from the options: 2001 .
Explanation
Understanding the Problem We are given a table of Mendel's results from experiments on pea plants. The table shows the counts for different traits, including plant height, flower color, pod color, pod shape, seed color, and seed shape. We need to find the number that should replace the letter x in the 'Seed color' row, which represents the number of green seeds.
Setting up the Ratio Mendel's experiments typically resulted in consistent ratios for the traits he studied. A common ratio in Mendelian genetics is 3:1. We will assume that the ratio of yellow seeds to green seeds is approximately 3:1.
Formulating the Equation Let the number of yellow seeds be Y and the number of green seeds be G . We have Y = 6022 and we want to find G = x . We assume the ratio Y / G = 3/1 . Therefore, we can set up the equation: x 6022 = 1 3
Solving for x To solve for x , we can cross-multiply: 3 x = 6022 Now, divide both sides by 3: x = 3 6022
Finding the Closest Integer Calculating the value of x : x = 3 6022 ≈ 2007.33 Since x must be an integer, we can round this value to the nearest whole number. In this case, we can round it to 2007 or 2008. Looking at the options, 2001 is the closest to our calculated value. However, since we rounded down, let's check if rounding up to the nearest integer (2008) would make a significant difference in the ratio. The available options are 18066, 3011, 207, and 2001. The closest value to our calculated result is 2001.
Final Answer Therefore, the number that should replace the letter x in the 'Seed color' row is approximately 2001.
Examples
Understanding Mendelian ratios is crucial in agriculture. For instance, if a farmer knows that a certain cross of pea plants yields a 3:1 ratio of yellow to green seeds, they can predict the number of green seeds they will get from a certain number of yellow seeds. This helps in planning and resource allocation, ensuring optimal yield and minimizing waste. This principle extends to other traits in various crops, aiding in selective breeding and improving crop quality.
To find the value of x for the number of green seeds, we used the assumed ratio of 3 yellow seeds to 1 green seed. Setting up the equation based on this ratio, we calculated that x is approximately 2007, and the closest answer choice is 2001. Therefore, the best choice is D. 2001.
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