Study Guide Review
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Start with forming an equation for each gym.
System of Equations:
T(x)=40x+140 M(x)=60x
Number of Months: 7
Cost: 420
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.
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).
Substitute ( 2,220) & ( 4,300)
Subtract terms
Calculate quotient
The slope for T(x) is 40. T(x)= 40x+ b We will now substitute the point (2,220) in the above equation in order to determine the y-intercept b.
x= 2, T(x)= 220
Multiply
LHS-80=RHS-80
Rearrange equation
The y-intercept is 140. With this, we have everything we need to form an equation. T(x)= 40x+ 140
We will now write an equation, y=M(x), for Mickey's Gym. Let's use (2,120) and (4,240) as our coordinate pairs to determine the slope.
Substitute ( 2,120) & ( 4,240)
Subtract terms
a/1=a
The slope of M(x) is 60. M(x)= 60x+ b Let's find the y-intercept by substituting the point (2,120) in the above equation.
x= 1, M(x)= 45
Multiply
LHS-120=RHS-120
Rearrange equation
We found the y-intercept to be 0, and thus we can write our second equation. M(x)= 120x+ 0
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.
Both gyms charge same amount for 7 months of membership.
The cost of 7 months of membership is $420.