Question

mr Green has altogether 100 dung beetles and spiders in his collection. the creatures have a total of 740 legs. dung beetle is 6 legged and spider is 8 legged. how many dung beetles and spiders does Mr. green have?

Answer 1

By setting up a system of equations, we can determine that Mr. Green has 30 dung beetles and 70 spiders in his collection.

Step-by-step explanation:

Let's solve the problem of finding out how many dung beetles and spiders Mr. Green has in his collection, based on the total number of creatures and the total number of legs. We know there are 100 creatures in total and they have 740 legs altogether. Dung beetles have 6 legs each, while spiders have 8 legs each.

We can set up a system of equations to represent this information. Let 'd' be the number of dung beetles and 's' be the number of spiders. Then:

1. d + s = 100 (the total number of creatures)
2. 6d + 8s = 740 (the total number of legs)

We can solve these equations simultaneously. If we multiply the first equation by 6, we get:

1. 6d + 6s = 600

Now, we subtract this from the second equation to solve for 's':

1. 6d + 8s = 740
2. 6d + 6s = 600
3. 2s = 740 - 600
4. 2s = 140
5. s = 70

There are 70 spiders in the collection. We can now find the number of dung beetles by subtracting the number of spiders from the total number of creatures:

1. d + 70 = 100
2. d = 100 - 70
3. d = 30

Mr. Green has 30 dung beetles and 70 spiders in his collection.