System of Equations:
T(x)=40x+140 M(x)=60x Number of Months: 7 Cost: 420
Practice makes perfect
We have two gyms, each with different prices for different numbers of months of membership.
Month
2
4
6
8
Tony's Gym
$220
$300
$380
$460
Mickey's Gym
$120
$240
$360
$480
We can write the equations for the costs of each gym 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 Tony's Gym
Let's start with the equation for Tony's Gym, y=T(x). In order to determine its slope, we will use the coordinate pairs (2,220) and (4,300).
We found the y-intercept to be 0, and thus we can write our second equation.
M(x)= 120x+ 0
System of Equations
We will write a system of linear equations using the equations we have written above.
T(x)=40x+140 & (I) M(x)=120x+0 & (II)
We want to know in how many months both memberships will cost the same. To do so, we need to solve the equation T(x)=M(x).
T(x)&=M(x)
40x+140&=120x
Let's use inverse operations to isolate the x-variable.
