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## 'Food Chains' printed from http://nrich.maths.org/

Fast solutions:

a.

15000 caterpillars,

1500 birds

500 tigers.

b. They are getting $\frac{42}{75}$ = 56 % of what could get.

c. 10000 caterpillars = 1000 birds = 333 tigers, 267 tigers would starve.

d. 89286 tigers

Detailed solutions:

a. The ratio is 1 bush : 30 caterpillars : 3 birds : 1 tiger, so with 500 bushes,

500 x 30 = 15000 caterpillars,

500 x 3 = 1500 birds,

500 x 1 = 500 tigers.

b. Lets say one bush contains 100 energy points. Then the caterpillars eat it, and have 75 points available to them. The birds get 75% of these points, 56 points, so the tiger has 42 points available to it. From eating the bush it could have obtained 75 points, so it's
obtaining 42/75 = 56 % of what it could get.

c. We still have 500 bushes but now we have 10000 caterpillars, so

10000 x 10 = 1000 birds

10000/30 = 333 tigers

The new numbers would be the equilibrium point, 267 tigers would starve.

d. 500 bushes give 500 x 100 x 75 energy points. Tigers need 42 energy points, so the tiger population would increase to $\frac{500 \times 100 \times 75}{42}$ = 89286 tigers!

The caterpillar and bird populations would be left with no food and would decrease unless they found another source of food.