Question

Find the equation that best represents the following word problem: In a certain freshman class, the number of girls is 83 less than twice the number of boys (b). The total number of students in that freshman class is 259. How many boys and girls are in that class?

Answer 1

`g = 2b-83`

`b+g=259`

Number of boys = 114

Number of girls = 145

Explanation:

Let the number of boys in the class =
`b`

Now, as per question statement,

Number of girls is 83 less than twice the number of boys.

Representing in the form of equation.

Let number of girls =
`g`

`g = 2b-83 ....... (1)`

Also, given that total number of students in the class = 259

i.e.
`b+g=259`

Putting value of
`g` using equation (1):

`\Rightarrow b+2b-83=259\\\Rightarrow 3b-83=259\\\Rightarrow 3b=259+83\\\Rightarrow 3b=342\\\Rightarrow \bold{b=114}`

So, number of boys, b = 114

Putting value of
`b` in equation (1) to find the value of
`g`.

`\Rightarrow g = 2(114)-83 \\\Rightarrow g = 228-83\\\Rightarrow \bold{g = 145}`

So, number of girls, g = 145.

Hence, the answer is:

Number of boys = 114

Number of girls = 145