Explanation: To determine the total number of free nucleotides in the chain, we need to calculate the number of adenine (A), cytosine (C), guanine (G), and thymine (T) nucleotides in the chain.
Given that the chain contains 750 nucleotides and the subtraction between adenine nucleotides (A) and cytosine nucleotides (C) is 300, we can set up the following equations:
A - C = 300 (Equation 1)
A + C + G + T = 750 (Equation 2)
We know that in DNA, adenine pairs with thymine (A-T) and cytosine pairs with guanine (C-G). Therefore, the number of adenine nucleotides (A) should be equal to the number of thymine nucleotides (T), and the number of cytosine nucleotides (C) should be equal to the number of guanine nucleotides (G).
From Equation 1, we have:
A = C + 300
Substituting this value into Equation 2, we get:
(C + 300) + C + G + (C + 300) = 750
3C + G + 600 = 750
3C + G = 150 (Equation 3)
Since the chain is for the transfer of four molecules of DNA, we know that the number of adenine nucleotides (A) and thymine nucleotides (T) combined should be four times the number of cytosine nucleotides (C). Thus, we can write:
A + T = 4C
Substituting A = C + 300 and T = A, we get:
(C + 300) + A = 4C
A = 3C - 300 (Equation 4)
Now, let's substitute Equation 4 into Equation 3 to solve for C and G:
3C - 300 + G = 150
3C + G = 450 (Equation 5)
We have two equations now, Equations 3 and 5, with two unknowns (C and G). Solving this system of equations will give us the values of C and G.
By solving Equations 3 and 5 simultaneously, we find that C = 150 and G = 300.
Now, we can find the value of A and T using Equation 4:
A = 3C - 300 = 3(150) - 300 = 150
Since the number of adenine nucleotides (A) is equal to the number of thymine nucleotides (T), we have:
T = A = 150
Finally, we can calculate the total number of free nucleotides:
Total = A + C + G + T = 150 + 150 + 300 + 150 = 750
Therefore, the total number of free nucleotides in the chain is 750