Making Equations to Solve a Problem-HELP, PLEASE

[1calculus1]

Making Equations to Solve a Problem----HELP, PLEASE!

Homework Statement

Hi,

I am in dire need of your help. I can't seem to solve this problem:

While it is a common knowledge that Martians are green and have seven heads, few people realize that a Martian has eleven eyes. At a recent party, while I was conversing with a Martian, I innocently remarked that if one-half of the Martians at the party suddenly became Earthlings (while the other half remained Martians), there would be 295 eyes at the party. Somewhat offended, the Martian noted that if one-half of the Earthlings at the party became Martians (while the other half stayed Earthlings), there would be 410 heads at the party. How many Martians and how many Earthlings were at the party?

Here's my trial on this:
7h+11e= martians

1/2(7h+11e) +1/2=295 eyes
1/2 + 1/2(7h+11e)= 410 heads
Then do the subtraction method from the linear equation to find one variable and go from there. The thing is I don't think my two equations are right because if I do that then all of the stuff on the left side will be 0 which is justly wrong.

CAN ANYONE HELP ME GET THOSE TWO EQUATIONS PLEASE? I know that 7h+11e= martians though. I just don't know how to go further.


Every little help counts. Please.



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ANOTHER QUESTION: (that I need help on)

For years George and Martha Huber supplemented their modest income by
blackmailing their neighbours. Neither of them made very much money at this until
two years ago, when Martha found out about Susan Black’s sordid past. That year,
George and Martha together extorted $108,000. The following year Revenue
Canada found out about Martha, so although she took in the same amount of
money, she had to pay half of it in taxes. Meanwhile, George’s activities went
unnoticed, and he took in $3000 more than he had the year before. Together they
netted $65,000. If Susan was paying Martha $75,000, how much Martha was
getting from other neighbours?

My tackle on this one:
G= George's share of the money
M= Martha's share of the money

(3000+G) + (1/2M)=108,000
G+M= 65,000

I don't know if those equations are right. PLEASE HELP!

Homework Equations

The Attempt at a Solution

 

[redargon]

for the first Q:

You have martians described as 7h+11e (remember to define your variables... ie. let h be number of heads and let e be number of eyes, before you continue. Later on you'll find that e has a different meaning in mathematics and is rarely used as a variable)
You have not, however described humans. What is the equation for a human (in terms of heads and eyes)?
Then you may be able to continue with your simultaneous equations.

Q2)
I think you're on the right track, but: (again list define your variables)
G+M=108000 (what they made last year together)
G+3000+1/2M=65000 (what they made this year together)

From this you can calculate what each made (last year) and then answer the rest of the question, ie. how much Martha got form other neighbours

or

G+M=65000 (what they made this year together)
G-3000+2M=108000 (what they made last year together)

From this you can calculate what each made (this year) and then answer the rest of the question, ie. how much Martha got form other neighbours

Notice how it changes depending on how you define your variables!