Question

Students who attend Washington Middle School are either in seventh or eighth grade. At the end of the first semester 25% of the students at Washington Middle School were on the honor roll. Seventh graders represented 60% 60 % of the students on the honor roll. If 124 124 students on the honor roll were in eighth grade, how many students attend Washington Middle School? ​ ​ There are students who attend Washington Middle School.

Answer 1

Answer:

There are 1240 students who attended Washington Middle School.

Step-by-step explanation:

Given:

Students who attend Washington Middle School are either in seventh or eighth grade.

At the end of the first semester 25% of the students at Washington Middle School were on the honor roll.

Seventh graders represented 60% of the students on the honor roll.

If 124 students on the honor roll were in eighth grade.

Now, to find the students attend Washington Middle School.

Let the total number of students be $x.$

So, the students at Washington Middle School were on the honor roll:

25% of $x$

$=\frac{25}{100} \times x$

$=\frac{25x}{100}$

$=\frac{x}{4}$

As, given seventh graders represented 60% of the students.

So, the students on the honor roll represented as seventh graders:

$60\%\ of\ \frac{x}{4}$

$=\frac{60}{100} \times \frac{x}{4}$

$=0.6\times \frac{x}{4}$

$=\frac{0.6x}{4}$

As, 124 students on the honor roll were in eighth graders.

Thus,

According to question:

$\frac{x}{4} -\frac{0.6x}{4} =124$

$\frac{x-0.6x}{4} =124$

$\frac{0.4x}{4} =124$

Multiplying both sides by 4 we get:

$0.4x=496$

Dividing both sides by 0.4 we get:

$x=1240.$

Therefore, there are 1240 students who attended Washington Middle School.