Calculations it Is Necessary to Show Intermediate

¶ … calculations it is necessary to show intermediate steps and formulas used, not just the final answer. Showing your work allows partial credit to be awarded in case the final answer is wrong. To receive credit (even if the answer is correct), you must show your work.

Suppose that you start a business manufacturing and selling bicycles, and it costs you $5,000 to get started. You determine that each bicycle will cost

$400 to manufacture. Explain why the linear equation gives your total cost to manufacture x bicycles ( in dollars).

x= number of bicycles sold y= total cost to manufacture x number of bicycles

The linear equation representing that relationship would be: y= 5000 + 400x.

A linear equation gives the total cost to manufacture x bicycles because it accounts for the $5,000 in start-up costs and then adds in the $400 per bicycle cost.

You decide to sell each bike for $600. What expression in x represents the revenue you will take in if you sell x bikes? Write an equation using to express your revenue when you sell x bikes ( in dollars).

x= number of bicycles sold y= total revenue

Therefore, the equation is: y= 600x

32. Form a system from the two equations in Exercises 30 and 31, and then solve

the system, assuming y1 =y2, that is, cost =revenue y= 5000 + 400x

y= 600x

600x= 5000 + 400x

600x -- 400x = 5000

200x= 5000

x=25

y= 600x

y=$15,000

33. The value of x from Exercise 32 is the number of bikes it takes to break even.

Fill in the blanks: When 25 bikes are sold, the break-even point is reached.

At that point, you have spent $15,000 dollars and taken in $15,000 dollars.

34. During their opening weekends, Spider-Man 3 and Shrek the Third

grossed a total of $272.7 million, with Spider-Man 3 grossing

$29.5 million more than Shrek the Third. How much did each of these movies earn during their opening weekends?

(Source: www.boxofficemojo.com)

m= Spider-Man 3

t= Shrek the Thrid

m + t = 272.7

m = 29.5 + t

29.5 + t + t = 272.7

29.5 + 2t = 272.7

2t= 272.7 -- 29.5

2t = 243.2

t = 243.2 / 2

t= 121.6 million m = 29.5 + t m = 29.5 + 121.6

m = 151.1 million

35. Carly is a bank teller. At the end of a day, she has a total of 69 $5 and $10 bills. The total value of the money is $590. How many of each denomination does she have?

f = five dollar bills t = ten dollar bills f + t = 69

5f + 10t = 590

f= 69- t

5(69-t) + 10t = 590

295 -- 5t + 10t = 590

295 + 5t = 590

5t = 590-295

5t = 295

t= 295/5 = 59 tens f= 69-t f= 69-59= 10 fives

36-A wireless phone service charges $14.99 as a monthly charge and $0.30 per minute for local calls.

How much would you pay in a month when you made ten local calls of three minutes each?

Let C. represent your total monthly cost; assuming you made only local calls, did not receive any calls, and the total number of minutes you were on the phone is m, write the equation to find your monthly bill.

m= minutes in local calls m= 10 x 3= 30

C= 14.99 + .3m

C= 14.99 + .3*30

C = 14.99 + 9= $23.99

How can you tell that the relationship between C. And m follows a linear pattern?

You can tell it follows a linear pattern because it is a first order equation involving two variables.

Graph the function that gives the total monthly cost and give the slope of the line.

y= mx + b is the slope intercept form of a linear equation. In the equation C= 14.99 + .3m, .3 is the slope and 14.99 is the y- intercept.