Systems of Equations: trouble with word problem  TOPIC_SOLVED

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Systems of Equations: trouble with word problem

Postby Siks123 on Wed Aug 15, 2012 3:33 pm

While I can solve the majority of word problems I'm having trouble with this one:

A textile mill produces fabric made from different fibers. From cotton, polyester, and nylon, the owners want to produce a fabric blend that will cost $3.25 per pound to make. The cost per pound of these fibers is $4.00, $3.00, $2.00, respectively. The amount of nylon is to be the same as the amount of polyester. How much of each fiber will be in the final fabric?

I tried the following system - I suppose I was off to a bad start because I couldn't find an answer:
Cotton = c
Polyester = p
Nylon = n

c+p+n=1 (1 fabric to be made from addition of the 3 fibers)
4c+3p+2n=3.25 (price)
3p+2n=0 (amount of nylon same as that of polyester)

Please help! Are any of the above equations correct? If not, how do we arrive at the correct system to solve?
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Re: Systems of Equations: trouble with word problem

Postby maggiemagnet on Wed Aug 15, 2012 4:11 pm

Siks123 wrote:A textile mill produces fabric made from different fibers. From cotton, polyester, and nylon, the owners want to produce a fabric blend that will cost $3.25 per pound to make. The cost per pound of these fibers is $4.00, $3.00, $2.00, respectively. The amount of nylon is to be the same as the amount of polyester. How much of each fiber will be in the final fabric?

I tried the following system - I suppose I was off to a bad start because I couldn't find an answer:
Cotton = c
Polyester = p
Nylon = n

Assuming that the variables stand for the amount of each then you can set "n" equal to "c" (e.g. substitute).

Siks123 wrote:4c+3p+2n=3.25 (price)

Rates don't add!! E.g. You can't add the price-per-pound of one fruit to the price-per-pound of another fruit to get the price-per-pound of a mixture of the fruits. So this equation is going to be a problem. Instead, you can use the method they show here.
:clap:
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Re: Systems of Equations: trouble with word problem  TOPIC_SOLVED

Postby LoveMath on Mon Sep 03, 2012 1:41 pm

Perhaps it's best to rewrite the question as: how much of each fabric must be used to get one pound of the mixed fabric? One thing we can start with is the fact that n=p since the amt. of nylon = amt. of polyester. Then,

(cost of C)(amt.of C) + (cost of P)(amt. of P) + (cost of N)(amt. of N) = (cost of mix)(amt of mix), where the amt of mix is 1 (i.e. 1 lb)
4C + 3P + 2N = 3.25(1), then since N = P we get
4C + 3N +2N = 3.25
4C + 5N =3.25 This is equation #1

We also have amt of C + amt of P + amt of N = 1
C + P + N =1, and since N=P we get
C + 2N = 1 or
C = 1-2N This is equation #2
Substituting 1-2N for C into equation #1 gives us

4(1-2N) + 5N = 3.25
4-8N+5N = 3.25
4 - 3N =3.25
-3N = - .75
N = .25 or 1/4 lb. then since N = P
P = 1/4 lb and thus we have 1/2 lb thus far, so the total fabric = 1lb,
C = 1/2 lb.

This does check out since 4(1/2) + 3(1/4) + 2(1/4)= 3.25(1)
2 + 3/4 + 2/4 = 3.25
2 + 5/4 =3.25
2 + 1.25 =3.25
Hope this helps!
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