Question

In a college art class, 76 students are painting a mural on one wall of the campus amphitheater. The wall has been divided into 21 sections, and each section will be painted by a group of either 2 or 4 students. How many more sections will be painted by a group of 4 students than by a group of 2 students?

Answer 1

Alternative B - 7.

Step-by-step explanation:

Let:

"a" be the number of sessions painted by a group of two students;

and

"b" be the number of sessions painted by a group of four students.

Since the number total of sessions is 23,

23 = a + b

Also, since the total of students is 76,

76= 2 × a + 4 × b

We can isolate "a" in the first equation and substitute in the second to find b:

a + b = 23

a = 23 - b

76= 2 (23 - b) + 4 × b

=> 76 = 46 - 2b + 4b

=> 76 - 46 = 2b

=> 30 = 2b

=> b = 30/2

=>b = 15

And, since a = 23 - b

a = 23 - 15

a = 8

Finally, how many more sessions are painted by 4-students group:

b - a

= 15 - 8

= 7

So, the 4-students group painted 7 more sessions.