contestada

Use the given cost table for the same product from two different companies to create a linear system.
Then solve the system to determine when the cost of the product will be the same and what the price will
be.
Two online spice retailers sell paprika by the pound using the following pricing chart.
Paprika (lb)
ISpice
16x)
$15.75
Spice Magic
s(x)
$23.25
1
2.
$34.50
$28.50
$41.25
3
$45.75
$57.00
4
$54.00
7(x)=1
+3
s(x) = 11.25x +
Both iSpice and Spice Magic charge $L
for
pounds of paprika.

Respuesta :

MrRoyal

The true statements are:

  • The linear equation for iSpace and Space Magic are [tex]y=11.75x +4[/tex] and [tex]y=10.25x+16[/tex] respectively
  • Both iSpice and Spice Magic charge $98 for 8 pounds of paprika.

What is a linear function?

The question is an illustration of a linear function; a linear function is a function that has a constant rate/slope

A linear function is represented as:

[tex]y=mx + c[/tex]

Where

  • m represents slope
  • c represents the y-intercept

Linear Equation of iSpice

Start by calculating the slope using:

[tex]m = \frac{y_2 -y_1}{x_2 -x_1}[/tex]

So, we have:

[tex]m = \frac{51 - 15.75}{4 -1}[/tex]

[tex]m = 11.75[/tex]

The linear equation is then calculated as:

[tex]y=m(x -x_1) + y_1[/tex]

So, we have:

[tex]y=11.75(x -1) + 15.75[/tex]

[tex]y=11.75x -11.75 + 15.75[/tex]

[tex]y=11.75x +4[/tex]

Linear Equation of Spice Magic

Start by calculating the slope using:

[tex]m = \frac{y_2 -y_1}{x_2 -x_1}[/tex]

So, we have:

[tex]m = \frac{57 - 26.25}{4 -1}[/tex]

[tex]m = 10.25[/tex]

The linear equation is then calculated as:

[tex]y=m(x -x_1) + y_1[/tex]

So, we have:

[tex]y=10.25(x -1) + 26.25[/tex]

[tex]y=10.25x -10.25 + 26.25[/tex]

[tex]y=10.25x+16[/tex]

The price, when both costs are the same

To do this, we simply equate both equations

[tex]11.75x +4 = 10.25x + 16[/tex]

Collect like terms

[tex]11.75x -10.25x = -4+ 16[/tex]

[tex]1.5x = 12[/tex]

Solve for x

[tex]x = 8[/tex]

Substitute 8 for x in any of the equations.

[tex]y=11.75 \times 8 +4[/tex]

[tex]y=98[/tex]

Hence, the price of both products will be the same at $98.00

Read more about linear equations at:

https://brainly.com/question/26227508

Otras preguntas