Question 1019851
let x equal the number of martians.
let y equal the number of earthlings.


each martian has 2 heads and 5 legs.
each earthling 1 head and 2 legs.


you have counted 29 heads and 67 legs at the party.


since each martian has 2 heads, then the number of martian heads at the party is equal to 2x.


since each earthling has 1 head, then the number of earthling heads at the party is equal to y.


you get 2x + y = 29


since each martian has 5 legs, then the number of martian legs at the party is equal to 5x.


since each earthling has 2 legs, then the number of earthling legs at the party is equal to 2y.


you get 5x + 2y = 67


you have 2 equations that need to be solved simultaneously.


they are:


2x + y = 29
5x + 2y = 67


multiply both sides of the first equation by 2 and leave the second equation as is and you get:


4x + 2y = 58
5x + 2y = 67


subtract the first equation from the second to get:


x = 9


when x = 9, 4x + 2y = 58 becomes 36 + 2y = 58
solve for y to get y = (58 - 36) / 2 = 22/2 = 11


you have x = 9 and y = 11.


there were 9 martians and 11 earthlings at the party.


9 martians give you 2*9 = 18 heads and 5*9 = 45 legs
11 earthlings gives you 1*11 = 11 heads and 2*11 = 22 legs


total heads = 11 + 18 = 29
total legs = 45 + 22 = 67


solution looks good.


solution is:


there were 9 martians and 11 earthlings at the party.