Expert: Richard J. Raridon - 3/15/2007

Question
Could you please help me on a few word problems?  It would be greatly appreciated.  I am trying to do them without a calculater and am trying to learn all steps, so I can do others.

1.  Fabric:  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, and $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?

2.  Taxes:  A company has taxable income of $312,000.  The federal tax is 25% of that portion left after the state tax has been paid.  The state tax is 10% of that portion left after the federal tax has been paid.  Find the federal and state taxes.

3.  Furniture sales:  A manufaurer of dining-room sets produces two styles:  early American and contemporary.  From past experience, management has determined that 20% more of the early American styles can be sold that the contemporary styles.  A profit of $250.00 is made on each early American set sold, whereas a profit of $350 is made on each contemporary set.  If, in the forthcoming year, management desires a total profit of $130,000. how many units of each style must be sold?

Thank you again for all your help!!


Answer
1. Let x = amt of cotton and y = amt. of nylon and amt. of polyester.  Then (4x+3y+2y)/(x+2y) = 3.25
which gives you x = 2y so x = 50% and y = 25%
2. 312000 -312000(0.75)(0.90) = $101,400
3. x = no. of contemporary styles so 1.2x = no. of early American styles
350x + 2.50(1.2x) = 130000
so x = 200 and 1.2x = 240