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DrKlahn, Hardware Engineer
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Experience:  BSci: Electrical Engr., Industrial Engr, and Computer Sci.
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# out of a box of parts there are 45 heads and 55 feet. a zerg

out of a box of parts there are 45 heads and 55 feet. a zerg has 1 head and 3 feet. a borg has 4 heads and 2 feet. how many zergs and how many borgs are there? please show steps to reach the answer.

DrKlahn :

A zerg has 1 head and 3 feet.

Let Z be the number of zergs.
Let B be the number of borgs.

There a 55 feet.

1Z + 4B = 45

Total number of feet:
3Z + 2B = 55

Multiply equation 1 by -3 to get:
-3Z + -12B = -135

Add this equation to equation 2:
0Z + -10B = -80

Divide by -10:
0Z + 1 B = 8

There are 8 borgs.
4B = 32, substitute this into equation 1
1Z + 32 = 45

Subtract 32 from both sides:
1Z = 13

There are 13 zergs and 8 borgs.
Check the work.

1Z + 4B = 45
1(13) + 4(8) = 45 correct!

3Z + 2B = 55
3(13) + 2(8) = 39 + 16 = 55 correct!

DrKlahn :

Let me know if anything is unclear.

DrKlahn :

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DrKlahn :

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DrKlahn :

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Customer:

this can not be correct because if there are 3 zorgs that times 1 head give me 3. 2 borgs times 4 heads gives me 8 which is a total of 11 heads not 45 heads.

DrKlahn :

There are 45 heads total, correct?

DrKlahn :

And a zerg has one head.

DrKlahn :

And a borg has 4 heads.

DrKlahn :

If the number of zergs is 13, there are 13 heads.

DrKlahn :

If the number of borgs is 8, there are 32 heads.

DrKlahn :

12 plus 32 is 45.

DrKlahn :

Sorry, 13 plus 32 is 45.

Customer:

sorry i didnt see your complete response, thanks you are correct...... sorry

DrKlahn :

No problem. That is why it is essential to check the answer afterwards. It is easy to make a mistake when adding equations in various signs.

DrKlahn :

Do you see the reasoning that led to the solution?

DrKlahn :

This is also visualizable as a geometric solution of the two following plane equations: X + 4Y = 45, 3X + 2Y = 55. Each equation defines a line in the X-Y plane. The point where the two lines intersect is the solution.

DrKlahn :

Do you have any questions? Don't hesitate to ask.

Customer:

not no at this time you have been a great help, thank you...

DrKlahn :

It's my pleasure, and you're very welcome. One moment while I unlock the Rating panel ...

DrKlahn :

Done. You can close this question whenever you're ready. Thank you for using JustAnswer today; our returning customers are the most valuable ones we have. I wish you a pleasant day and a good week upcoming.