The first bunch of bananas has one-fourth more bananas than the second bunch.…
2019
The first bunch of bananas has one-fourth more bananas than the second bunch. If the second bunch has 5 bananas less than the first bunch, then what is the number of bananas in the first bunch?
- A.
23
- B.
28
- C.
25
- D.
24
Attempted by 2 students.
Show answer & explanation
Correct answer: C
Concept: When one quantity is described as a fraction more than a second quantity, express the first quantity in terms of the second using that fraction, then use any given numeric difference between the two quantities to form one linear equation in one unknown and solve it.
Let the second bunch contain x bananas.
The first bunch has one-fourth more bananas than the second bunch, so the first bunch contains x + (1/4)x = (5/4)x bananas.
The second bunch has 5 bananas less than the first bunch, so (5/4)x minus x equals 5.
Simplify: (1/4)x = 5, so x = 20.
The first bunch therefore has (5/4) times 20, which is 25 bananas.
Cross-check: the second bunch has 20 bananas, and one-fourth more than 20 is 20 + 5 = 25, matching the first bunch; also 25 minus 20 equals 5, matching the stated gap. Both conditions hold together only for 25, confirming the first bunch has 25 bananas.