Question

In a garden there are some bees and flowers. If one bee sits on each flower then one bee will be left. If two bees sit on each flower then one flower will be left. Find the number of bees and number of flowers.

Answer 1

Hint:Here we assume number of bees and number of flowers as variables and form two equations for two different situations. We use the concept of greater than or less than in this question where we add or subtract the quantities to make it equal to the other quantity.
* If \[x\] is \[m\]more than \[y\], we write \[x = y + m\]because when we add \[m\]to RHS then it becomes equal to LHS.
* If \[x\] is \[m\]less than \[y\], we write \[x = y - m\]because when we subtract \[m\]to RHS then it becomes equal to LHS.

Complete step-by-step answer:
Let us assume the number of bees as \[x\].
Assume the number of flowers as \[y\].
When one bee sits on each flower then one bee will be left means that the number of bees is one more than the number of flowers when one bee sits on each flower.
Therefore, we can write \[x\] is greater than \[y\] by \[1\].
i.e. \[x = y + 1\] \[...(i)\]
Now, when two bees sit on each flower then one flower will be left means that one flower less than total flowers is occupied when two bees sit on each flower.
So number of flowers occupies is \[y - 1\]
Therefore, we can write twice the number of flowers occupied will be equal to number of bees
i.e. \[2(y - 1) = x\] \[...(ii)\]
Now we solve the equations \[(i),(ii)\]
From equation \[(i)\]\[x = y + 1\]
Substitute the value of \[x = y + 1\] in equation \[(ii)\]
\[
  2(y - 1) = y + 1 \\
  2y - 2 = y + 1 \\
 \]
Bring the variables to one side and constants to the other side.
\[
  2y - y = 1 + 2 \\
  y = 3 \\
 \]
Substitute the value of \[y = 3\] in equation \[(i)\]
\[x = 3 + 1 = 4\]
Therefore, the number of bees is \[4\] and the number of flowers is \[3\].

Note:Students are likely to get confused while adding and subtracting the more and less values respectively. Always add or subtract to the quantity that comes after the word ‘more than’ or ‘less than’ and equate it to the term that is written ‘more than’ or ‘less than’.