Roses and Bees
Algebra
Level
1
There are some roses in a garden and some bees are hovering over them.
- If every bee lands on a different rose, one of them won't get a rose.
- If every two bees share one rose, then there will be one rose left without any bees.
Which of the following is a possible number of roses and the number of bees in the garden?
1 Rose and 1 Bee
2 Roses and 4 Bees
3 Roses and 4 Bees
3 Roses and 5 Bees
5 Roses and 6 Bees
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Let the number of roses be R , and the number of bees be B .
The first equation tells us that B − 1 = R
The second equation tells us that B = 2 ( R − 1 ) .
Substituting the first equation into the second, we obtain 2 ( R − 1 ) − 1 = R ⇒ 2 R − 3 = R ⇒ R = 3 .
Thus B = R + 1 = 4 .
There are 3 roses and 4 bees.