Question

On an alien planet, there are two types of aliens: green aliens and purple aliens. Green aliens have 3 heads and purple aliens have 7 heads. At a recent alien meeting, there were 48 aliens present and a total of 220 heads. How many green aliens and purple aliens were in attendance? green aliens: purple aliens:

Answer 1

Total number of aliens = 48

Green aliens = G

Purple ALiens = P

P + G = 48

Green aliens = 3 heads

Purple Aliens = 7 heads

Total heads = 220

7P + 3G = 220

The system of equations:

P + G = 48 (a)

7P + 3G = 220 (b)

Solve (a) for P:

P = 48-G

Replace P on (b) and solve for G

7(48-G) + 3G = 220

336- 7G +3G =220

-7G+3G = 220-336

-4G = -116

G = -116/-4

G= 29

Replace G on (a) and solve for P

P +29 = 48

P = 48-29

P = 19

Green Aliens : 29

Purple Aliens : 19