A certain number of birds are sitting on two trees, A and B. If one bird moves…
2022
A certain number of birds are sitting on two trees, A and B. If one bird moves from tree B to tree A, the numbers of birds on the two trees become equal. However, if one bird moves from tree A to tree B, the number of birds on tree B becomes twice that on tree A. How many birds are there on trees A and B, respectively?
Answer: C. 5,7 — ConceptA word problem about two changing quantities can be modelled by assigning variables to the original quantities and translating each condition into an…
- A.
3,5
- B.
7,6
- C.
5,7
- D.
9,11
Show answer & explanation
Correct answer: C
Concept
A word problem about two changing quantities can be modelled by assigning variables to the original quantities and translating each condition into an equation.
Each transfer changes both quantities: the source decreases by 1 and the destination increases by 1. Solving the resulting simultaneous equations gives the original values.
Application
Let A and B denote the original numbers of birds on trees A and B.
When one bird moves from B to A, the counts become A + 1 and B − 1. Equality gives A + 1 = B − 1, so B = A + 2.
When one bird moves from A to B, the counts become A − 1 and B + 1. The second condition gives B + 1 = 2(A − 1).
Substitute B = A + 2: A + 3 = 2A − 2, hence A = 5. Therefore B = 5 + 2 = 7.
Cross-check
With (A, B) = (5, 7), moving a bird from B to A gives (6, 6), while moving a bird from A to B gives (4, 8), and 8 is twice 4.
Result
Thus the original numbers of birds are 5 on tree A and 7 on tree B.