Expert: Paul Klarreich - 9/13/2007

Question
1) A store advertised that during its Labor Day sale $15 will be deducted from every purchase over $100.  In addition, after the deduction is taken, the store offers and early-bird discount of 20% to any person who makes a purchase before 10 am If Hakeem makes a purchase of x dollars x>100 at 8 am, what, in terms of x is the cost of Hakeems purchase?

2) In a science experiment, when resistor A and resistor B are connected in a parallel circuit, the total resistance is 1/ (1/A + 1/B).  This complex fraction is equivalent to what?

Answer
Questioner:   Ruth
Category:  Calculus
Private:  No
 
Subject:  Math Pre-Calc
Question:  1) A store advertised that during its Labor Day sale $15 will be deducted from every purchase over $100.  In addition, after the deduction is taken, the store offers and early-bird discount of 20% to any person who makes a purchase before 10 am If Hakeem makes a purchase of x dollars x>100 at 8 am, what, in terms of x is the cost of Hakeems purchase?

2) In a science experiment, when resistor A and resistor B are connected in a parallel circuit, the total resistance is 1/ (1/A + 1/B).  This complex fraction is equivalent to what?
.................
Hi, Ruth,

1) Start off by writing:

Let x = THE ORIGINAL PRICE of the item.

Then you can write:

x - 15 = the cost after the Labor Day discount.

And, since a 20% discount is equivalent to multiplying the price by (100% - 20%) or (80%) or (0.8), you can write:

0.8(x - 15) = the final cost after both discounts.  Now what about that $3 off coupon that we got from Linens and Things?

..........................

2) In a science experiment, when resistor A and resistor B are connected in a parallel circuit, the total resistance is 1/ (1/A + 1/B).  This complex fraction is equivalent to what?

Well, it is equivalent to lots of things; that's the beauty of mathematics.  But I think you really want to ask:

How can this complex fraction be converted to an ordinary fraction -- one which does not contain fractions itself.

Simple: A. Find an LCD for all the denominators.   B. Multiply every term by that LCD.

In this case:

   1
----------
1     1
--- + ---
A     B

Your LCD is  AB.  So every term gets hit by AB:

    1(AB)
-------------
AB 1     1 AB
 --- + ---
  A     B

  1(AB)
----------
AB   AB
-- + --
 A    B

 AB
------
B + A

That's it.