Exercise 10 Page 436

There are two companies that sell road salt. Prices for different number of tons are shown below.

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 Company 1

Let's start with the equation for Company 1, y=A(x). In order to determine its slope, we will use the coordinate pairs (5,1775) and (10,3350).

Therefore, the slope for A(x) is 315. A(x)= 315x+ b We will now substitute the point (5,1775) in the above equation in order to determine the y-intercept b.

The y-intercept is 200. With this, we have everything we need to form an equation for the cost of the salt from Company 1. A(x)= 315x+ 200

Equation for Company 2

We will now write an equation, y=B(x), for Company 2. Let's use (5,2750) and (10,4000) as our coordinate pairs to determine the slope.

The slope of B(x) is 250. B(x)= 250x+ b Let's find the y-intercept by substituting the point (5,2750) in the above equation.

We found the y-intercept to be 1500 and thus we can write our second equation. B(x)= 250x+ 1500

System of Equations

We will write a system of linear equations using the equations we have written above. A(x)=315x+200 & (I) B(x)=250x+1500 & (II) We want to determine the number of tons, x, for which both companies charge the same. To do so, we need to solve the equation A(x)=B(x). A(x)&=B(x) 315x+200&=250x+1500 Let's use inverse operations+ to isolate the x-variable.

Both companies charge same amount for 20 tons of road salt.

Calculating the Price

We can find the price of 20 tons of road salt by substituting 20 for x in either of the equations. Let's do this using A(x).

Both companies charge $6500 for 20 tons of salt.