SOLUTION: Hi, I have a word problem I need help with. Four friends have different numbers of cows on their farms. Jorge has 3 times as many cows as Carla. Marcus has half as many cows as Jo

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Question 1047410: Hi, I have a word problem I need help with.
Four friends have different numbers of cows on their farms. Jorge has 3 times as many cows as Carla. Marcus has half as many cows as Jorge. Dominick has 2 less than 4 times as many cows as Carla. How many cows does each person have if they have a total of 169 cows?
I'm having a problem with the equations of Marcus and Dominik.And I'm not sure how to write the equations of either of them. But isn't Carla "X", and Jorge " 3X"?
Thank you.
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Assign variables that help to make sense of the problem and LITERALLY form the equations the way the description says. Nothing mysterious. 
PERSON        HOW MANY COWS
Jorge           j
Carla           c
Marcus          m
Dominick        d

Transcribe the description:
system%28j=3c%2Cm=j%2F2%2Cd=4c-2%2Cj%2Bc%2Bm%2Bd=169%29
From here, you have more than one way to go. Various ways of substituting; or some use of Elimination Method, or matrix row reduction operations.

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REMOVED SECTION CONTAINING MISTAKE
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TRY AGAIN TRYING AGAIN
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Initial system was system%28j=3c%2Cm=j%2F2%2Cd=4c-2%2Cj%2Bc%2Bm%2Bd=169%29.
Subst for d.
system%28j=3c%2Cj=2m%2Cj%2Bc%2Bm%2B4c-2=169%29

system%28j=3c%2Cj=2m%2Cj%2B5c%2Bm=169%2B2%29

Substitute for j.
system%283c=2m%2C3c%2B5c%2Bm=171%29

system%283c=2m%2C8c%2Bm=171%29

Subst for m.
m=171-8c
-
3c=2%28171-8c%29
3c=342-16c
19c=342
c=342%2F19
highlight%28c=18%29---------Use this to find each variable in steps from here.

m=171-8c
m=171-8%2A18
highlight%28m=27%29----------Another result.

Keep going for the last two, j and d.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

Hi, I have a word problem I need help with.
Four friends have different numbers of cows on their farms. Jorge has 3 times as many cows as Carla. Marcus has half as many cows as Jorge. Dominick has 2 less than 4 times as many cows as Carla. How many cows does each person have if they have a total of 169 cows?
I'm having a problem with the equations of Marcus and Dominik.And I'm not sure how to write the equations of either of them. But isn't Carla "X", and Jorge " 3X"?
Thank you.
Yes, if Carla's number is X, then Jorge's is: 3X



Anyway, let's do it my way!

Let number of cows Carla has be C

Then Jorge has 3C

Marcus' count: matrix%281%2C5%2C+%281%2F2%29%2C+of%2C+3C%2C+or%2C+3C%2F2%29

Dominick's count: 4C - 2

Since the sum is 169, then we get: C+%2B+3C+%2B+3C%2F2+%2B+4C+-+2+=+169

8C+%2B+3C%2F2+-+2+=+169

8C+%2B+3C%2F2+=+171

16C + 3C = 342 ------- Multiplying by LCD, 2

19C = 342 

C, or Carla has:  

Jorge has: 3(18)

Marcus has: 3%2818%29%2F2

Dominick has: 4(18) - 2

I'm sure you're able to calculate the last 3.

See how easy that was? It's not COMPLEX at all.