Algebra problems
A bird has 2 legs, a cat has 4 legs, an insect has 6 legs and a spider has 8 legs.
Claire looks at some animals and counts all their legs.
She counts 38 legs.
There are twice as many birds as spiders and twice as many cats as insects.
How many of each type of animal can she see?
Well if b = the bird, c = the cat, i = the insect and s = the spider, B = 2S and C = 2i, we can make an equation.
ReplyDelete2(2S) + 8S + 4(2i) + 6i = 38
12S + 14i = 38
Now we now this, all we can do is just guess systematically.
First let's see when there are no spiders:
This will give us 14i = 38, which does not work.
Secondly, let's see when there is 1 spider:
This gives us 14i = 26, which again, won't work.
Thirdly, let's see when there are 2 spiders:
this gives us 14i = 14, which we can solve to get a whole number. It will give us i = 1. Now we can substitute the things we know into our first equation at figure out the solution. Try substituting for yourself!