Exercise 7 Page 436

Two online spice retailers sell paprika. Prices are given in the following table.

We can write the equations for the costs of each company in slope-intercept form. y= mx+ b In this form, m is the slope and b is the y-intercept. We will find each slope by using the Slope Formula. m=y_2-y_1/x_2-x_1 In the above formula, (x_1,y_1) and (x_2,y_2) represent pairs of data entries that satisfy the equation.

Equation for iSpice

Let's start with the equation for iSpice, y=S(x). In order to determine its slope, we will use the coordinate pairs (1,15.75) and (2,27.50).

Thus, the slope for S(x) is 11.75. S(x)= 11.75x+ b We will now substitute the point (1,15.75) in the above equation in order to determine the y-intercept b.

The y-intercept is 4. With this, we have everything we need to form an equation for the cost of paprika from iSpice. S(x)= 11.75x+ 4

Equation for Spice Magic

We will now write an equation, y=M(x), for Spice Magic. Let's use (1,26.25) and (2,36.50) as our coordinate pairs to determine the slope.

The slope of M(x) is 10.25. M(x)= 10.25x+ b Let's find the y-intercept by substituting the point (1,26.25) in the above equation.

We found the y-intercept to be 16 and thus we can write our second equation. M(x)= 10.25x+ 16

System of Equations

We will write a system of linear equations using the equations we have written above. S(x)=11.75x+4 & (I) M(x)=10.25x+16 & (II) We want to determine the amount of paprika, x, for which both companies charge the same. To do so, we need to solve the equation S(x)=M(x). S(x)&=M(x) 11.75x+4&=10.25x+16 Let's use inverse operations to isolate the x-variable.

Both companies charge the same amount for 8 pounds of paprika.

Calculating the Price

We can find the price of 8 pounds of paprika by substituting 8 for x in either of the equations. Let's do this using M(x).

Both companies charge $98 for 8 pounds of paprika.