Question

Pond Critters
Ms. Wilson sets up a pond water aquarium in the classroom. Ms. Wilson tells the class
there are five different kinds of aquatic animals in the aquarium. There are caddis fly
larvae, diving beetles, whirligig beetles, dragonflies and tadpoles.
Ms. Wilson says one-twelfth of the pond animals are dragonflies. One-third of the
animals are caddis fly larvae. One-fourth are tadpoles. There are the same number of
diving beetles as whirligig beetles. If there are six dragonflies, how many pond critters
are in the aquarium? How many caddis fly larvae, tadpoles, diving beetles and whirligig
beetles are in the aquarium? Show all your mathematical thinking.

Answer 1

Answer: There are 72 pond critters  in the aquarium. There are 24 caddis fly larvae, 18 tadpoles, 12 diving beetles and 12 whirligig  beetles in the aquarium.

Step-by-step explanation:

Given :  There are caddis fly  larvae, diving beetles, whirligig beetles, dragonflies and tadpoles in the aquarium

One-twelfth of the pond animals are dragonflies

One-third of the  animals are caddis fly larvae.

One-fourth are tadpoles.

The same number of  diving beetles as whirligig beetles.

Number of dragon flies = 6

Let the total animals are = x, dragon flies are represented by d , caddis fly larvae as c, tadpoles as t , diving beetles as b and whirligig beetles as w.

Now : x = d + c + t+ b + w

$\frac{1}{12}\times x=d$    (1)

$\frac{1}{3}\times x=c$    (2)

$\frac{1}{4}\times x=t$   (3)

$b=w$      (4)

$d=6$       (5)

Comparing 1 and 5

$\frac{1}{12}\times x=6////x=72$

Thus pond critters are 72.

$c=\frac{1}{3}\times 72=24$

$t=\frac{1}{4}\times 72=18$  

$d=6$

Now x = d + c + t+ b + w

72 = 6+24+18+b+b   (as b= w)

2b =24

b = 12

Thus w = 12.