Question

In a college archaeology class, 78 students are going to a dig site to find and study artifacts. The dig site has been divided into 24 sections, and each section will be studied by a group of either 2 or 4 students. How many of the sections will be studied by a group of 2 students?

Answer 1

Answer: There are 9 sections of group of 2 and 15 sections of group of 4.

Step-by-step explanation:

Since we have given that

Let the number of sections of group of 2 students be 'x'.

Let the number of sections of group of 4 students be 'y'.

So,total number of sections = 24

According to question, it becomes,

$x+y=24----------------(1)$

Number of students going to dig = 78

So, it becomes,

$2x+4y=78\\\\x+2y=39---------------(2)$

From, eq(1), we get that

$x=24-y$

Put in EQ(2), we get that

$x+2y=39\\\\24-y+2y=39\\\\y=39-24\\\\y=15$

So, the value of x is $24-15=9$

Hence, there are 9 sections of group of 2 and 15 sections of group of 4.