Question 1019851: Martians have two heads and five legs. There was a "meet and greet" party that had both Martians and Earthlings. At that party I counted 29 heads and 67 legs. How many Martians and Earthlings were at the party?
Found 3 solutions by josmiceli, Theo, LinnW:
Answer by josmiceli(19441)   (Show Source):
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! 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.
Answer by LinnW(1048)  (Show Source):
You can put this solution on YOUR website! Set M = number of Martians
Set E = number of Earthlings
2*M + E = 29, that is two times number Martians plus the number of Earthlings
5*M + 2E = 67, 5 times the number of Martians plus 2 times Earthlings = no. of legs
2M + E = 29
5M + 2E = 67
Adjust 2M + E = 29 by adding -2M to each side
E = 29 - 2M
Substitute (29 - 2M) for E in 5M + 2E = 67
5M + 2(29 - 2M) = 67
5M + 58 -4M = 67
M + 58 = 67
add -58 to each side
M = 9
Since E = 29 - 2M
E = 29 - 2(9)
E = 29 - 18
E = 11
Checking our original equations,
2*M + E = 29, 2*9 + 11 = 29 , 18 + 11 = 29, so this checks.
5*M + 2E = 67, 5*9 +2*11 = 67 , 45 + 22 = 67, so this checks.
We have 9 Martians and 11 Earthlings.
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