Long word problem!!!

Question

Every Forisie has exactly 4 eyes and exactly 2 legs.  Every Forlegie has exactly 4 legs and exactly 1 eye.  A gathering of Forisies and Forlegies has an equal number of eyes and legs.  

 

What is the minimum of aliens present? 

Answer 1

Let's suppose that you had x forisie. That makes 4x eyes and 2x legs.

Let's suppose that you had y forlegie. that makes y eyes and 4y legs.

 

When they're in the same room you've got 4x + y eyes and 2x + 4y legs.

But we want to know when the number of eyes = the number of legs....so,

4x + y = 2x + 4y 

2x = 3y   or y= 2/3 x

 

So we have to choose x's that wont lead to fractions....any multiple of 3 will cancel out the denominator of 3. So I'll make a table.

x   3   6   9   12   15    18    21

y   2   4   6    8     10    12    14

 

These all work but the minimum is 2 forisie and 3 forlegie.

 

CHECK    

3 forisie have 12 eyes and 6 legs 

2 forlegie have 2 eyes and 8 legs 

 

TOTAL in the group.....14 eyes and 14 legs.