System of Equations:
R(x)=35.99x+120.25 S(x)=39.99x+20.25
Both companies charge $1020 for 25 cases of paper towels.
Practice makes perfect
There are two companies that sell paper towels. The prices for different number of cases are shown in the table.
Paper Towels (cases)
Restaurant Warehouse
Supply Side
5
$300.20
$220.20
10
$480.15
$420.15
15
$660.10
$620.10
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 Restaurant Warehouse
Let's start with the equation for Restaurant Warehouse, y=R(x). In order to determine its slope, we will use the coordinate pairs (5,300.20) and (10,480.15).
Thus, the slope for R(x) is 35.99.
R(x)= 35.99x+ b
We will now substitute the point (5,300.20) in the above equation in order to determine the y-intercept b.
The y-intercept is 120.25. With this, we have everything we need to form an equation for the cost of paper towels from Restaurant Warehouse.
R(x)= 35.99x+ 120.25
Equation for Supply Side
We will now write an equation, y=S(x), for Supply Side. Let's use (5,220.20) and (10,420.15) as our coordinate pairs to determine the slope.
We found the y-intercept to be 20.25 and thus we can write our second equation.
S(x)= 39.99x+ 20.25
System of Equations
We will write a system of linear equations using the equations we have written above.
R(x)=35.99x+120.25 & (I) S(x)=39.99x+20.25 & (II)
We want to determine the number of cases, x, for which both companies charge the same. To do so, we need to solve the equation R(x)=S(x).
R(x)&=S(x)
35.99x+120.25&=39.99x+20.25
Let's use inverse operations to isolate the x-variable.
