Algebra review problems?

Question

I have these inequality problems i need help setting up. thanks. I can do them, i just need help setting them up.

1. A company manufactures and sells blank audiocassette tapes. the weekly fixed cost is $10,000 and it costs $0.40 to produce each tape. the selling price is $2.00 per tape. How many tapes must be produced and sold each week for the company to generate a profit.

2. To earn an A in a course, you must have a final average of at least 90%. On the first 4 exams, you have grades of 86%, 88%, 92%, and 84%. If the final exam is worth 2 grades, what must you get on the final to earn an A in the course?

3. On 2 exams you have grades of 86 and 88. there is an optional final exam, which counts as 1 grade. you decide to take the final in order to get a course grade of an A, meaning a final average of at least 90.

a. what must you get on the final to earn an A in the course?

b. by taking the final, if you do poorly, you might risk the B that you have in the course based on the first 2 exams. If your final average is less than 80, you will lose your B in the course. Describe the grades on the final that will cause this to happen.

4. The toll to a bridge is $3. A 3-month pass costs. $7.50 and reduces the toll to $.50. A 6-month pass costs $30 and permits crossing the bridge for no additional fee. How many crossings per 3-month period does it take for the 3-month pass to be the best deal?

Answer 1

1. Fixed cost (per week): $10,000

    Variable cost (per tape): $0.40

    Revenue (per tape): $2.00

so, in order to make a profit, the company has to have revenue that exceeds its fixed and variable costs. In other words, figure out how many weeks of revenue ($2 - $0.40) would be needed to exceed $10,000.

2. Use trial and error to find out what score you would need on the final to average out at 90%. Average is found by adding the final (5th score) to the other scores, and dividing by 5.

3. see above.

4.  Consider the fixed and variable costs for the 3-month pass, versus the fixed cost of the 6-month pass.

Answer 2

1. 10000+.4x < 2x   solve for x

2. (86 + 88 + 92 + 2x)/5 > 90

3.a (86+88 + x)/3 >90

3.b (86+88 + x)/3 < 80

4.  30 < 7.5 + .5x < 3x