The average number of visitors to a library in the first 4 days of a week was…
2024
The average number of visitors to a library in the first 4 days of a week was 58. The average number of visitors for the 2nd, 3rd, 4th and 5th days was 60. If the number of visitors on the 1st and 5th days were in the ratio 7:8, what was the number of visitors on the 5th day?
- A.
56
- B.
58
- C.
62
- D.
64
Show answer & explanation
Correct answer: D
Concept
When two equal-sized groups overlap so that exactly one member leaves the group and one new member joins in its place, the difference between the two group totals equals the difference between the value of the member who joined and the value of the member who left. Also, when a known difference is split in a given ratio, the difference between the ratio's two parts corresponds to that known difference, which lets each part's actual value be found.
Application
The average number of visitors for Day 1 to Day 4 is 58, so their total is 58 x 4 = 232.
The average number of visitors for Day 2 to Day 5 is 60, so their total is 60 x 4 = 240.
Day 2, Day 3 and Day 4 are common to both totals; the only change between the two groups is that Day 1 leaves and Day 5 joins. So (Day 5) minus (Day 1) = 240 - 232 = 8.
The visitors on Day 1 and Day 5 are in the ratio 7 : 8, so let Day 1 = 7k and Day 5 = 8k.
Then Day 5 - Day 1 = 8k - 7k = k, and since this difference is 8, k = 8.
So the number of visitors on Day 5 = 8k = 8 x 8 = 64.
Cross-check
With k = 8, Day 1 = 7k = 56. Then Day 2 + Day 3 + Day 4 = 232 - 56 = 176 from the first average, and also = 240 - 64 = 176 from the second average -- the two independent calculations agree, confirming that the Day 5 count is 64.