Making Eqns to Solve Probs: Martians have 11 eyes;

[1434runescape]

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!

 

[mmm4444bot]

7h + 11e = martians This equation looks like garbage, to me.

Hi there:

Thank you for showing your work, but you did not define your symbols h and e.

I could assume that h stands for heads and e stands for eyeballs. If so, then your equation states the following.

"The number of martians at the party is equal to the sum of seven times heads plus eleven times eyeballs."

Clearly, that does not make sense. The number of martians is not a function of the sum of heads and eyeballs. It's the other way around. The number of heads and eyeballs at the party is a function of the number of martians and earthlings at the party.

Let's start over.

The first thing to do with a word problem is to identify what unknowns you need to find.

Hopefully, you realize that you need to find two different unknowns in this exercise.

The second thing to do is to assign variable names for the unknown(s).

I'll do that for you.

LET m = the number of martians at the party

LET p = the number of people at the party

(If you use variable names that make sense intuitively, it helps. First, I chose e for earthlings, but I don't want others to get e confused with eyeballs, so I decided to choose a different name. Next, I thought of h for humans, but that could potentially be confused with heads. DARN IT! With a little more effort, I settled on p for people.)

With these variables names, the total number of heads and eyeballs could be expressed as follows. (These equations will not be used in this exercise; I type them only for you to see how the variable names could be used.)

Total heads at the party = 7m + p

Total eyeballs at the party = 11m + 2p

Now that you have good variable names with which to work, set up two equations in m and p that state the given information.

Hint: There are (1/2)m + (1/2)m martians at the party.

Hint: There are (1/2)p + (1/2)p people at the party.

Cheers,

~ Mark

PS: You can run, but you can't escape!

 

[mmm4444bot]

For years George and Martha Huber each supplemented their modest income by individually blackmailing their neighbours. Neither of them made very much money (so sad) 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 last year. If Susan was paying Martha $75,000 during each of the last two years, then how much was Martha getting each year during the same interval from the other blackmailed neighbours combined?

My tackle on this one:

G = George's share of the money

M = Martha's share of the money

(3000 + G) + (1/2M) = 108000

G + M = 65000

Hello Run Escape:

Nope. You got the amounts backwards.

Firstly, I would reword the definitions of G and M.

G = George's supplemental income two years ago

M = Martha's supplemental income two years ago

(Note: Martha's supplemental income did not change over the past two years, but that does not matter.)

The expression G + M represents their combined supplemental income two years ago, not last year. Otherwise, your equations look good.

I also note that my previous instruction to assign a variable name for the unknown(s) in a word problem does not really apply in this second exercise because it's much easier to find G and M first, followed by calculating the answer to this second exercise using G.

In other words, this exercise is an exception to the "rule" that I first posted, and you did good.

Cheers,

~ Mark



NEWS FLASH: The bodies of Martha and George Huber were discovered in their penthouse apartment yesterday morning by their team of housekeepers who arrived for work at 0800 hours. According to the RCMP, it appears to be a murder-suicide. Mr. Huber was apparently poisoned; Ms. Huber died of a single gunshot wound to the head.