The first gym charges $4 a session plus a one-time $50 fee. In total, the cost is 4x+50 4x = cost of the x sessions (x is some whole number) 50 = flat fee y = 4x+50 = total cost
Similarly, the second gym has a cost equation of y = 6x+30 6x = cost of the x sessions (6 dollars a session) 30 = one time fee 6x+30 = total cost
Set the two x expressions equal to each other and solve for x 4x+50 = 6x+30 4x+50-30 = 6x+30-30 ... subtract 30 from both sides 4x+20 = 6x 4x+20-4x = 6x-4x 20 = 2x 2x = 20 2x/2 = 20/2 x = 10
So it takes 10 sessions for the two gyms to have the same cost
Answer: 10
====================================================================== Problem 37)
First we need the slope Let (x1,y1) = (3,0) and (x2,y2) = (5,3) So,x1=3 and y1=0 x2=5 and y2=3
Plug those four items into the slope formula to get m = (y2 - y1)/(x2 - x1) m = (3 - 0)/(5 - 3) m = 3/2
Now use one of the points, say (x,y) = (3,0), to find the y intercept b y = mx+b 0 = (3/2)*3+b 0 = 9/2+b 0-9/2 = b b = -9/2
So m = 3/2 and b = -9/2
The equation is therefore y = (3/2)x - 9/2
====================================================================== Problem 38)
Slope = m = -3 The point the line goes through is (x,y) = (5,-9) so x = 5 and y = -9 pair up
y = mx+b -9 = -3*5+b -9 = -15+b -9+15 = -15+b+15 6 = b b = 6
The y intercept is b = 6
Since we know m = -3 and b = 6 we go from this y = mx+b to this y = -3x+6
Answer: y = -3x+6
====================================================================== Problem 39)
x = number of weeks y = total cost
Accountant A: y = 60x+100 Plug in x = 5 y = 60x+100 y = 60*5+100 y = 300+100 y = 400 So accountant A will charge a total of $400 for the 5 weeks
Accountant B: y = 20x+500 Plug in x = 5 y = 20x+500 y = 20*5+500 y = 100+500 y = 600 So accountant B will charge a total of $600 for the 5 weeks
Coach Johnson should go with accountant A since this is the cheaper option (the coach will save $200).
