Question

An electronics store discovers that it can sell 5 televisions per day by pricing them at $150. When the televisions are on sale for $100 the store sells 10 of them every day. Write a linear equation to compare the price of a television, p, to the number sold, x. Then write a quadratic equation to compare the revenue, m, from selling televisions to the number sold, x.

Answer 1

Answer:

$p=-10x+200$

$m = -10x^2+200x$

Step-by-step explanation:

Given : An electronics store discovers that it can sell 5 televisions per day by pricing them at $150. When the televisions are on sale for $100 the store sells 10 of them every day.

To Find: Write a linear equation to compare the price of a television, p, to the number sold, x. Then write a quadratic equation to compare the revenue, m, from selling televisions to the number sold, x.

Solution:

Let p be the price and x be the no. of television sold

We are given that  it can sell 5 televisions per day by pricing them at $150. When the televisions are on sale for $100 the store sells 10 of them every day. i.e(5,150) and (10,100)

Now to find the linear equation to compare the price of a television, p, to the number sold, x.

We will use two point slope form

Formula : $y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

$(x_1,y_1)=(5,150)$

$(x_2,y_2)=(10,100)$

Substitute the values in the formula

$y-150=\frac{100-150}{10-5}(x-5)$

$y-150=\frac{-50}{5}(x-5)$

$y-150=-10(x-5)$

$y-150=-10x+50$

$y=-10x+50+150$

$y=-10x+200$

x is the no. of television sold

y is the price

Since p denotes the price

So,  $p=-10x+200$

Thus a linear equation to compare the price of a television, p, to the number sold, x is   $p=-10x+200$

Now $Revenue = Cost \times quantity$

Since price of x telivisons = $p=-10x+200$

So,  $Revenue = (-10x+200) \times x$

$Revenue = -10x^2+200x$

m denotes revenue

So,$m = -10x^2+200x$

Thus a quadratic equation to compare the revenue, m, from selling televisions to the number sold, x. is $m = -10x^2+200x$

Hence a linear equation to compare the price of a television, p, to the number sold, x is   $p=-10x+200$ and a quadratic equation to compare the revenue, m, from selling televisions to the number sold, x. is $m = -10x^2+200x$

Answer 2

Answer:

$p = -10x + 200$

$m = -10x^2 +200x$

Step-by-step explanation:

We know that at a price of $ 150, 5 televisions are sold and at a price of $ 100, 10 televisions are sold.

We must write a linear equation for this situation.

The equation of the line will have the following form

$p = mx + b$

Where m is the slope of the line and b is the intercept with the p axis

$m=\frac{y_2-y_1}{x_2-x_1}\\\\m=\frac{100-150}{10-5}=-10$

$b=p_1-mx_1\\\\b=150-(-10)(5)\\\\b=200$

The equation is:

$p = -10x + 200$

Now we know that the revenue m is the product of the price p for the quantity sold x.

$m = p * x$

$m=(-10x + 200)*x$

$m = -10x^2 +200x$