Problem 36)
x = number of sessions
y = cost
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
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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
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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
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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).
