c Set the equations from Parts A and B equal to each other and solve for m.
D
d The total usage should equal 20 months.
A
a C(m)=60m+800
B
b C(m)=40m +1200
C
c 20 months
D
d 7.5 years
Practice makes perfect
a The cost of the Super Cool X1440 will depend on the initial cost and the cost per month. Since the cost per month is constant, the equation must show a straight line.
C(m)=am+b
In this equation, a is the line's slope and b is the initial cost. The initial cost is the purchasing price of the machine, b=800. The slope is the increase in cost per month, a=60. Now we can write the equation.
C(m)=60m+800
b The equation describing Efficient Energy Model is also a straight line because the cost increases at a constant rate. We know that the machine costs b=1200 to purchase and an additional a=40 per month to keep it running. Now we can write the equation.
C(m)=40m+1200
c We want to know how many months it takes before the equations gives the same value. Therefore, we should set them equal to each other and solve for m.
It will take 20 months for your family to compensate for the additional cost of the more expensive machine.
d If the machine is only used for 4 months per year, and it takes 20 months in total to earn back the money you spend on the expensive machine, it must take 204=5 years to earn back the money.
