Read the following information carefully and answer the question that follows.

The information presents the attendance of adults and students at a science center over three days (Friday, Saturday, and Sunday). A total of 200 visitors attended the center across all three days. The number of adults who visited on Sunday is 60% of the number of students who visited on Friday. The number of students who visited on Sunday is 10 fewer than the number of students who visited on Friday. On Saturday, 40 adults and 50 students visited the center. The ratio of the total visitors on Sunday to Saturday is 3 : 5.

What is the total number of students who visited the science center across all three days?

The correct option is 120.

Step 1: Calculate the total number of visitors on Saturday and Sunday.
On Saturday, 40 adults and 50 students visited the center.

$\text{Total visitors on Saturday}=40+50=90$

The ratio of total visitors on Sunday to Saturday is given as 3 : 5. We can find total Sunday visitors as:

$\text{Total visitors on Sunday}=\frac{3}{5}\times 90=54$

Step 2: Determine the number of students who visited on Friday.
Let the number of students who visited on Friday be S_F.

From the problem details for Sunday:
• Adults on Sunday = 60% of students on Friday = 0.6 S_F
• Students on Sunday = 10 fewer than students on Friday = S_F - 10

Since total visitors on Sunday equals 54, we set up the equation:

$0.6S_F+(S_F-10)=54$

Simplifying the algebraic equation step-by-step:

$1.6S_F-10=54$

$1.6S_F=64$

$S_F=\frac{64}{1.6}=40$

So, 40 students visited on Friday.

Step 3: Calculate the total number of students across all three days.
• Students on Friday = 40
• Students on Saturday = 50
• Students on Sunday = 40 - 10 = 30

Summing these values gives:

$\text{Total students}=40+50+30=120$

Therefore, the total number of students who visited the science center across all three days is 120.