Answer :
Answer:
[tex]p = -10x + 200[/tex]
[tex]m = -10x^2 +200x[/tex]
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
[tex]p = mx + b[/tex]
Where m is the slope of the line and b is the intercept with the p axis
[tex]m=\frac{y_2-y_1}{x_2-x_1}\\\\m=\frac{100-150}{10-5}=-10[/tex]
[tex]b=p_1-mx_1\\\\b=150-(-10)(5)\\\\b=200[/tex]
The equation is:
[tex]p = -10x + 200[/tex]
Now we know that the revenue m is the product of the price p for the quantity sold x.
[tex]m = p * x[/tex]
[tex]m=(-10x + 200)*x[/tex]
[tex]m = -10x^2 +200x[/tex]
Answer:
[tex]p=-10x+200[/tex]
[tex]m = -10x^2+200x[/tex]
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 : [tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
[tex](x_1,y_1)=(5,150)[/tex]
[tex](x_2,y_2)=(10,100)[/tex]
Substitute the values in the formula
[tex]y-150=\frac{100-150}{10-5}(x-5)[/tex]
[tex]y-150=\frac{-50}{5}(x-5)[/tex]
[tex]y-150=-10(x-5)[/tex]
[tex]y-150=-10x+50[/tex]
[tex]y=-10x+50+150[/tex]
[tex]y=-10x+200[/tex]
x is the no. of television sold
y is the price
Since p denotes the price
So, [tex]p=-10x+200[/tex]
Thus a linear equation to compare the price of a television, p, to the number sold, x is [tex]p=-10x+200[/tex]
Now [tex]Revenue = Cost \times quantity[/tex]
Since price of x telivisons = [tex]p=-10x+200[/tex]
So, [tex]Revenue = (-10x+200) \times x[/tex]
[tex]Revenue = -10x^2+200x[/tex]
m denotes revenue
So,[tex]m = -10x^2+200x[/tex]
Thus a quadratic equation to compare the revenue, m, from selling televisions to the number sold, x. is [tex]m = -10x^2+200x[/tex]
Hence a linear equation to compare the price of a television, p, to the number sold, x is [tex]p=-10x+200[/tex] and a quadratic equation to compare the revenue, m, from selling televisions to the number sold, x. is [tex]m = -10x^2+200x[/tex]