Question

1. mrs. brewers class has b boys and g girls. the number of boys is 10 greater than one - third the number of girls. there are a total of 34 students in mrs. brewers class. which of the following equations could help solve this problem?

Explanation:

Step1: Analyze the number of boys

The number of boys \( b \) is 10 greater than one - third the number of girls \( g \). So, we can write the equation for \( b \) as \( b=\frac{1}{3}g + 10\).

Step2: Analyze the total number of students

The total number of students in the class is the sum of the number of boys and the number of girls. We know that the total number of students is 34, and since the number of boys is \( b=\frac{1}{3}g + 10\), we can substitute \( b \) in the equation \( b + g=34\) with \( \frac{1}{3}g + 10\).
So the equation becomes \( (\frac{1}{3}g + 10)+g = 34\). We can also simplify this equation:
First, combine like terms: \( \frac{1}{3}g+g+10 = 34\), and \( \frac{1}{3}g+\frac{3}{3}g+10=34\), which is \( \frac{4}{3}g + 10=34\).
If we want to write it in terms of \( b \) and \( g \) directly from the two conditions:

1. From "the number of boys is 10 greater than one - third the number of girls": \( b-\frac{1}{3}g=10\)
2. From "total of 34 students": \( b + g=34\)

We can solve this system of equations. For example, from the second equation \( b = 34 - g\), and substitute into the first equation: \( (34 - g)-\frac{1}{3}g=10\), which can be rewritten as \( 34-\frac{4}{3}g = 10\) or \( \frac{4}{3}g=34 - 10=24\)

Answer:

The system of equations (or the single - variable equation after substitution) that can help solve the problem is:

• \( b-\frac{1}{3}g = 10\) and \( b + g=34\) (system of linear equations)
• Or the single - variable equation \( \frac{4}{3}g+10 = 34\) (after substituting \( b=\frac{1}{3}g + 10\) into \( b + g=34\))