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.
Find the total number of students who visited the science center on Friday and adults who visited on Saturday combined.
Correct Answer :
80
Solution :
The correct answer is 80.
Step 1: Find total visitors on Saturday and Sunday.
On Saturday, 40 adults and 50 students visited the science center.
Total visitors on Saturday = 40 + 50 = 90.
The ratio of total visitors on Sunday to Saturday is given as 3 : 5.
Therefore, total visitors on Sunday = 90 × (3 / 5) = 54.
Step 2: Find total visitors on Friday.
A total of 200 visitors attended the center across all three days.
Total visitors on Friday = 200 - (Saturday visitors + Sunday visitors)
Total visitors on Friday = 200 - (90 + 54) = 200 - 144 = 56.
Step 3: Find the number of students who visited on Friday.
Let the number of students who visited on Friday be SF.
From the given information:
1. Adults who visited on Sunday = 60% of students on Friday = 0.6 × SF
2. Students who visited on Sunday = SF - 10
Total visitors on Sunday = Adults on Sunday + Students on Sunday
Thus, 40 students visited the science center on Friday.
Step 4: Calculate the required combined total.
We need to find the total number of students on Friday and adults on Saturday combined:
- Students on Friday = 40
- Adults on Saturday = 40
Combined total = 40 + 40 = 80.
Therefore, the total number of students who visited on Friday and adults who visited on Saturday combined is 80.
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