Parallelograms are four sided figures that have two pairs of opposite, parallel sides. Quadrilateral ABCD shown below is parallelogram. One of it's two diagonals, AC is drawn and it's midpoint M is located. Use tracing paper in this problem to help you answer the following questions.

a)

number of flying insects                       number of butterflies

           1                                                                 9/25

           50                                                               18

          100                                                             36

b)

162 butterflies

Step-by-step explanation:

Let 'x' denotes the variable such that 36x denotes the number of butterflies and 100x denotes the number of flying insects and the ratio of butterflies to total number of flying insects is 36 to 100 (i.e. ).

As there are total 450 flying insects.

This means that 100x=450

⇒  x=4.5 ( since on dividing both side of the equality by 100).

Hence the number of butterflies are 36x=162.----(1).

(a)

Since for 1 flying insect 100x=1

⇒  x=1/100

Hence 36 x=36×(1/100)=36/100=9/25

for 50 flying insects.

100x=50

⇒ x=1/2

Hence, 36x=36×(1/2)=18

Similarly is the way to compute for 100 flying insects.

   number of flying insects                       number of butterflies

           1                                                                 9/25

           50                                                               18

          100                                                             36

(b)

In the conservatory there are 162 butterflies.( as computed above in equation (1))