Question

11) In a college art class, 76 students are painting a mural on one wall of the compus ampnicaThe wall has been divided into 23 sections, and each section will be painted by a group of eitr2 at 4 students. How many more sections will be painted by a group of 4 students than by agroup or 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\cdot a+4\cdot b`

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

`\begin{gathered} a+b=23 \\ a=23-b \end{gathered}`
`\begin{gathered} 76=2\cdot(23-b)+4\cdot b \\ 76=46-2b+4b \\ 76-46=2b \\ 30=2b \\ b=(30)/(2) \\ b=15 \end{gathered}`

And, since a = 23 - b

`\begin{gathered} a=23-15 \\ a=8 \end{gathered}`

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

`\begin{gathered} b-a \\ 15-8 \\ =7 \end{gathered}`

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

Answer: Alternative B - 7.