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After two years on the​ job, an​ engineer's salary was $40,000. After seven years on the​ job, her salary was $40150.
Let y represent her salary after x years on the job. Assuming that the change in her salary over time can be
approximated by a straight​ line, give an equation for this line in the form y = mx + b.
 

 
Solution
40150 – 40000 / 5 = 30x
40150 – 40000 / 5 = 30 > 40000 – 2(30) = 39940
30x + 39,940
  The cost of owning a home includes both fixed costs and variable utility costs.
Assume that it costs $2,660.00 per month for mortgage and insurance payments, and it costs an average of
$4.64 per unit for natural​ gas, electricity, and water usage. Determine a linear equation that computes the
annual cost of owning this home if x utility units are used.
 

Solution
x = average = 4.64x
2660 x 12 = 31,920
   
The change in a certain​ engineer's salary over time can be approximated by the linear equation
y = 1500x + 7500 where y represents salary in dollars and x represents number of years on the job.
According to this​ equation, after how many years on the job was the​ engineer's salary $52,000​?
 

Solution
52000 = 1500x + 47500
52000 – 1500x + 47500
52000 – 47500 = 4500
4500 = 1500x = 3
   
Let the demand and supply functions be represented by​ D(p) and​ S(p), where p is the price in dollars.
Find the equilibrium price and equilibrium quantity for the given functions.
D(p) = 2184 – 50p
S(p) = 160p – 546
 

 
Solution
2184 – 50p = 160p – 546
2184 + 546 = 2730 and 160p + 50p = 210p
210p = 2730 so 2730 / 210 = 13
2184 – (13 x 50) = 1534
  Suppose that the demand and price for a certain model of graphing calculator are related by
p = D(q) = 104 - 3.5q where p is the price​ (in dollars) and q is the demand​ (in hundreds).
Find the price if the demand is 100 calculators.

 
Solution
104 – 3.5 = $100.50
 

 

Suppose that the price and supply for a certain model of graphing calculator are related by p = S(q) = 4q
where p is the price​ (in dollars) and q is the supply​ (in hundreds) of calculators.
Find the supply if the price is $87. Round to the nearest whole number if necessary.

Solution
q = p / 4 =
87 / 4 (87 / 4) =         21.75
in thousands =       21.75 · 1,000 =        2,175  
A book publisher found that the cost to produce 1000 calculus textbooks is $26300,
while the cost to produce 2000 calculus textbooks is $51500.
Assume that the cost C(x) is linear function of x, the number of textbooks produced.
What is the marginal cost of a calculus textbook?

Solution
51500 – 26300 = 25,200
25200 / 1000 = $25.20

Northwest Molded molds plastic handles which cost ​$1.00 per handle to mold.
The fixed cost to run the molding machine is $3,345 per week. If the company sells the handles for
$4.00 ​each, how many handles must be molded weekly to break​ even?

Solution
3345 / 4 – 1 =
3345 / 3 = 1115

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