Exam 2: B: Review and Applications of Algebra

Solve the following pair of equations. Verify your solution. g - h = 17

Sears reported that its sales in January were down 17.4% from its sales in December. What percentage were December sales of January sales?

Simplify and collect like terms:

Solve for the unknown rounded to two decimal places

Gamma Corp. manufactures and sells widgets for $6.00 each. Therefore, its total revenue, TR, from the sale of X widgets in a year is TR = $6X It costs Gamma $2 for materials and labour to produce each widget. In addition, Gamma expects to incur $80,000 of other costs during a year. Therefore, Gamma's total costs for the year, TC, are expected to be -720TC = $2X + $80,000 Gamma's expected net income, NI, for the year will be NI = TR - TC = $6X - ($2X + $80,000) = $4X - $80,000 a) What is the slope and TR-intercept of a TR vs. X plot? b) What is the slope and TC-intercept of a TC vs. X plot? c) What is the slope and NI-intercept of an NI vs. X plot? d) Which of the three plotted lines is steepest? e) How much does NI increase for each widget sold? f) If Gamma were able to reduce its materials and labour cost to $1.75 per widget, state for each plotted line whether its slope would increase, decrease, or remain unchanged.

How much is $102 after a decrease of 2%?

Solve: 1.25y - 20.5 = 0.5y - 11.5

At a United Way fund raiser, students sold cinnamon buns for $2 each or 3 for $5. They sold 500 all together, and raised $900. How many of the 3 for $5 were sold?

What amount after a reduction of equals $549?

Simplify and collect like terms: 1 - (3x - xy + y) - (-x + y - 5xy)

Sam has $20,000 to invest. He invested part at 5% and part at 6%. His investments earned $1,120 total interest for the year. How much did Sam invest at each rate?

If operating expenses are 25% of revenue, by what percentage does revenue exceed operating expenses?

A manufacturing firm pays monthly salaries of $3,400 to each production worker and $2,800 to each assembly worker. As the economy drops into a recession, the firm decides to reduce its total monthly manufacturing payroll from $253,800 to $198,000 by laying off 20% of its production workers and 25% of its assembly workers. How many layoffs will there be from each of the assembly and production divisions?

Sales have increased by 10% over last year. What percentage less was last year's sales than this year's sales?

The retail price of All Natural Granola dropped from $7.98 to $7.29 when the package size was reduced from 700 g to 600 g. What was the percent change in the unit price?

Solve the following pair of equations. Verify your solution. 0.33e + 1.67f = 292 1.2e + 0.61f = 377

Calculate the missing value: Initial Value = 0.043; Final Value =?; Percent Change = -30%

What number is 25% less than 96?

Calculate the final result to two decimal places, where x = $6.80

Evaluate the following: