Question 1204546: Studio A Studio B
classes|cost Classes|cost
3 70 4 80
7 130 6 120
8 145 9 180
12 205 11 220
The tables above show the cost of yoga classes at two different studios. Studio A charges a mat fee of $25, but Studio B has no initial fee. Write a system of equations that will determine when the two studios cost the same. Found 2 solutions by math_tutor2020, MathLover1:Answer by math_tutor2020(3817) (Show Source):
Studio A Studio B
classes|cost Classes|cost
3 70 4 80
7 130 6 120
8 145 9 180
12 205 11 220
x = number of classes
y = total cost
Two ordered pairs with studio A are: (3,70) and (7,130)
Let's use the slope formula on those points.
The slope 15 means the cost goes up $15 each time you take a new class.
In other words, studio A charges $15 per class. This is on top of the $25 mat fee.
We arrive at the equation
As a check, plug in x = 3 and you should get the result y = 70. I'll let the student do this confirmation and check the other values as well.
Follow similar steps for studio B and you should get
The system of equations is therefore
x = number of classes
y = total cost
Studio | | | | |
slope
Studio has no initial fee, so ....eq.2
a system of equations
....eq.1 ....eq.2
---------------------------left sides are equal, so
the two studios cost the same if the number of classes is 5
check
Studio ....eq.1
|
5|100
(