To solve the problem, we need to determine the number of boys given the ratio of girls to boys and the number of girls.
1. Understanding the Ratio: The ratio of girls to boys is given as 2:3. This means for every 2 girls, there are 3 boys.
2. Given Information: We know that the number of girls is 14.
3. Setting Up the Relationship:
- According to the ratio, let the number of boys be [tex]\( B \)[/tex].
- The number of girls [tex]\( G \)[/tex] to the number of boys [tex]\( B \)[/tex] is [tex]\( \frac{2}{3} \)[/tex].
- Given [tex]\( G = 14 \)[/tex].
4. Setting Up the Proportion:
[tex]\[
\frac{G}{B} = \frac{2}{3}
\][/tex]
Substituting the given number of girls:
[tex]\[
\frac{14}{B} = \frac{2}{3}
\][/tex]
5. Solving the Proportion:
To find [tex]\( B \)[/tex], we can cross-multiply to get:
[tex]\[
14 \times 3 = 2 \times B
\][/tex]
This simplifies to:
[tex]\[
42 = 2B
\][/tex]
6. Isolating [tex]\( B \)[/tex]:
Divide both sides of the equation by 2:
[tex]\[
B = \frac{42}{2}
\][/tex]
[tex]\[
B = 21
\][/tex]
Therefore, the number of boys is [tex]\( 21 \)[/tex].
So, the correct answer is [tex]\( D. 21 \)[/tex].
