Expert: Chanda Walker - 4/5/2009

Question
I have a question about word problems.  The problem states that a vendor is selling doughnuts. If he prices them at 1.50 sales will reach 73 per day, if priced at 2.00 then sales drop to 51 per day. Write a linear equation using y for the number of doughnuts sold at x dollars each. I was setting up problem as (x)(y) = total sold, but a linear equation cannot be expressed as (x)(y). I am confused? or something.

Answer
If you graphed this, you'd have these points:

(1.50, 73)
(2.00, 51)

The slope of this line is:  (73 - 51)/(1.50 - 2.00) = -22/.50 = -44

Now we should find the y intercept . . .

51 = -44 * 2.00 + b
51 = -88 + b
b = 139

So the equation is:

y = -44 x + 139

Let's check that . . .

73 ?=? -44 * 1.50 + 139
73 ?=? -66 + 139
73 = 73

y = -44x + 139 is our linear equation.

Let me know if I can help further.