There are some bees in a garden. One-fifth of them went to a particular…
2025
There are some bees in a garden. One-fifth of them went to a particular flower, one-third of them went to another flower, three times the difference of these two fractions went to a third flower, and one bee remained, roaming around alone. How many bees were there in total?
- A.
15
- B.
20
- C.
96
- D.
85
Show answer & explanation
Correct answer: A
Concept: In a ‘parts of a whole’ word problem, every described portion is written as a fraction or multiple of the unknown total, and since every unit is accounted for in exactly one part, the sum of all the parts must equal the total itself.
Application: Let the total number of bees be r.
One-fifth of the bees went to the first flower: r/5.
One-third of the bees went to the second flower: r/3.
The difference between these two parts is r/3 − r/5 = (5r − 3r)/15 = 2r/15, so three times this difference went to the third flower: 3 × 2r/15 = 6r/15 = 2r/5.
One bee remained on its own, so this last part contributes 1.
Every bee belongs to exactly one of these four parts, so their sum equals the total: r/5 + r/3 + 2r/5 + 1 = r.
Combine the fractional terms over a common denominator of 15: 3r/15 + 5r/15 + 6r/15 + 1 = r, i.e. 14r/15 + 1 = r.
Isolate r: r − 14r/15 = 1, so r/15 = 1, giving r = 15.
Cross-check: With r = 15, the first flower gets 15/5 = 3 bees, the second gets 15/3 = 5 bees, their difference is 2, so the third flower gets 3 × 2 = 6 bees, and 1 bee remains alone. Total = 3 + 5 + 6 + 1 = 15, which matches r, confirming the total is 15.