# Linear Equation Worded Problem

• Mar 4th 2013, 06:58 PM
Fratricide
Linear Equation Worded Problem
The cost, \$C, of manufacturing each jacket of a particular type is given by the formula

C = an + b for 0 < n ≤ 300

where a and b are constants and n is the size of the production run of this type of jacket.

For making 100 jackets, the cost is \$108 each.
For making 120 jackets, the cost is \$100 each.

a) Find the values of a and b.
b) Sketch the graph of C against n for 0 < n ≤ 300.
c) Find the cost of manufacturing each jacket if 200 jackets are made.
d) If the cost of manufacturing each jacket is \$48.80, find the size of the production run.

If someone could point me in the right direction it would be much appreciated.
• Mar 4th 2013, 07:18 PM
chiro
Re: Linear Equation Worded Problem
Hey Fratricide.

Please show us what you have tried and what you have thought about to solve the problem.
• Mar 4th 2013, 07:46 PM
Fratricide
Re: Linear Equation Worded Problem
Initially I thought that I could substitute some values, so I did 108 = 100a + b and tried solving for a and b but got hideously incorrect answers, and from there I have come to you.
• Mar 4th 2013, 09:51 PM
ibdutt
Re: Linear Equation Worded Problem
Make the other equation for production of 120 jackets and get the values for a and b. thereafter everything will fall in its place.
• Mar 5th 2013, 02:19 AM
Fratricide
Re: Linear Equation Worded Problem
Not quite sure I understand what you mean?
• Mar 5th 2013, 06:14 AM
ibdutt
Re: Linear Equation Worded Problem
108 = 100a + b
100 = 120a + b
This will give a = -2/5 and b = 148
• Mar 5th 2013, 03:02 PM
Fratricide
Re: Linear Equation Worded Problem
Thanks for your help. From there I was able to finish the question... mostly. The part of the question asking me to sketch the graph has me stumped. I thought I knew what I was doing, but then a wild 28 appeared! http://i.imgur.com/TElqRR7.jpg
Where does the 28 come from?
• Mar 6th 2013, 01:32 AM
Fratricide
Re: Linear Equation Worded Problem
Bump!
• Mar 6th 2013, 03:32 AM
ibdutt
Re: Linear Equation Worded Problem
What appears to me is that he has just rtaken the production size to be 300 for the purpose of graph, though we can draw the graph in the absence of the point ( 300 , 28 )