Question

A manufacturing company finds that they can sell 250 items at $3.50 per item and 350 items at $2.50 per item.

If the relationship between the number of items sold a and the price per item p is a linear one:
Find a formula that gives a in terms of p: x =

Now use the formula to find the number of items they will sell if the price per item is $1.50.
They will sell…
items if the price is $1.50.

Answer 1

• a = 600 -100p
• a = 450 for p = 1.50

Explanation:

You want the formula that represents (p, a) = (3.50, 250) and (2.50, 350) as a linear function. Then you want the value of 'a' for p = 1.50.

Slope

We can see from the ordered pairs that 'a' goes up by 100 when p goes down by 1.00. The slope is ...

m = ∆a/∆p = 100/(-1) = -100

Intercept

The y-intercept (b) can be found by solving the slope-intercept equation for b:

y = mx +b

b = y - mx

For (x, y) = (3.50, 250), the value of 'b' is ...

b = 250 -(-100)(3.50) = 600

Equation

The slope-intercept equation for 'a' in terms of p is ...

a = -100p +600

Evaluation

The value of 'a' for p = 1.50 is ...

a = -100(1.50) +600

a = 450

They will sell 450 items if the price per item is $1.50.