What percentage of a DNA double helix will be adenine (A) if 30 percent of the nitrogenous bases are guanine (G)?

Understand the Problem

The question is asking for the percentage of adenine in a DNA double helix based on the provided information that 30 percent of the nitrogenous bases are guanine. Since the percentages of adenine and thymine are equal, and guanine pairs with cytosine in a DNA molecule, we can use the known percentage of guanine to find the percentages of the other bases.

Answer

$20\%$

Steps to Solve

Identify the percentage of cytosine (C)

We know that in a DNA double helix, guanine (G) pairs with cytosine (C). Therefore, the percentage of cytosine will be equal to the percentage of guanine. Since 30% of the nitrogenous bases are guanine, this means that:

$$ \text{C} = 30% $$

Set up the percentage equation for adenine (A) and thymine (T)

In DNA, the percentage of adenine (A) is equal to the percentage of thymine (T). Let's denote the percentage of adenine (and thymine) as $x$. Therefore, we can write the equation for the total percentages of the nitrogenous bases as follows:

$$ \text{A} + \text{T} + \text{G} + \text{C} = 100% $$

Substituting the known values, we have:

$$ x + x + 30% + 30% = 100% $$

Simplify and solve for x (percentage of A and T)

This simplification yields:

$$ 2x + 60% = 100% $$

Now, subtract 60% from both sides:

$$ 2x = 40% $$

Next, divide both sides by 2:

$$ x = 20% $$

This means that both adenine and thymine are 20%.

The percentage of adenine in the DNA double helix is $20%$.

More Information

In DNA, the base pairing rules state that adenine pairs with thymine and guanine pairs with cytosine. This means the total base composition must always balance out, leading to the same amount of adenine as thymine, and guanine as cytosine.

Tips

Forgetting that adenine and thymine percentages are equal can lead to incorrect calculations. Remember to denote them with the same variable, such as $x$.
Miscalculating the remaining percentage by not appropriately combining the known values.

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