To solve this word problem, let's break it down step-by-step and set up the correct equation.
1. Understanding the Problem:
- Let [tex]\( b \)[/tex] represent the number of boys in the class.
- The number of girls is 83 less than twice the number of boys.
- The total number of students in the class is 259.
2. Setting up the Equation:
We know that the total number of students is the sum of boys and girls:
[tex]\[
b + (\text{number of girls}) = 259
\][/tex]
According to the problem, the number of girls is 83 less than twice the number of boys:
[tex]\[
\text{number of girls} = 2b - 83
\][/tex]
Now, substitute this expression into the total number of students equation:
[tex]\[
b + (2b - 83) = 259
\][/tex]
3. Solving the Equation:
Simplify the equation:
[tex]\[
b + 2b - 83 = 259
\][/tex]
Combine like terms:
[tex]\[
3b - 83 = 259
\][/tex]
Add 83 to both sides to isolate the term with [tex]\( b \)[/tex]:
[tex]\[
3b = 259 + 83
\][/tex]
[tex]\[
3b = 342
\][/tex]
Divide both sides by 3 to solve for [tex]\( b \)[/tex]:
[tex]\[
b = \frac{342}{3}
\][/tex]
[tex]\[
b = 114
\][/tex]
4. Finding the Number of Girls:
Substitute [tex]\( b = 114 \)[/tex] back into the expression for the number of girls:
[tex]\[
\text{number of girls} = 2b - 83
\][/tex]
[tex]\[
\text{number of girls} = 2(114) - 83
\][/tex]
[tex]\[
\text{number of girls} = 228 - 83
\][/tex]
[tex]\[
\text{number of girls} = 145
\][/tex]
So, the number of boys in the class is 114, and the number of girls is 145.
