Correct Option
Let F represent the number of flowers and B represent the number of bees.
According to the first condition, "If one bee lands on each flower, one bee will be left out." This implies that the total number of bees is one more than the total number of flowers. B = F + 1 (Equation 1)
According to the second condition, "If two bees land on each flower, one flower will be left out." This means that all bees occupy (F - 1) flowers, with two bees on each occupied flower. B = 2(F - 1) (Equation 2)
Equating Equation 1 and Equation 2 to solve for F: F + 1 = 2(F - 1) F + 1 = 2F - 2 1 + 2 = 2F - F 3 = F
Substitute the value of F back into Equation 1 to find B: B = 3 + 1 B = 4
Thus, the number of flowers is 3 and the number of bees is 4.
Incorrect Options
The correct number of flowers and bees are 3 and 4, respectively. Let's examine why the other options are incorrect based on the given conditions:
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Option 1: 2 and 4 (Flowers = 2, Bees = 4)
If there are 2 flowers and 4 bees:
- Condition 1: If one bee lands on each flower, 2 bees land, leaving 4 - 2 = 2 bees left out. This contradicts the condition that one bee is left out.
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Option 2: 3 and 2 (Flowers = 3, Bees = 2)
If there are 3 flowers and 2 bees:
- Condition 1: If one bee lands on each flower, 2 bees land, leaving 3 - 2 = 1 flower empty. This contradicts the condition that one bee is left out.
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Option 4: 4 and 3 (Flowers = 4, Bees = 3)
If there are 4 flowers and 3 bees:
- Condition 1: If one bee lands on each flower, 3 bees land, leaving 4 - 3 = 1 flower empty. This contradicts the condition that one bee is left out.