Solve the following problems showing all your work every step of the way.
1. You have been given information that if a student is a resident and they enroll for more than 12 hours, then their tuition will equal $120 plus $10 per hour for every hour greater than 12. Create an equation that would allow a student to simply plug in their number of hours enrolled and calculate their tuition. Give a specific example to show your equation works.
2. Research: There are many formulas that are used in our everyday lives. Use the library or the internet to research an example of a formula, explain the variables of the formula, and show a specific example by plugging in values for the particular formula.
3. Set up three different equations that have the solution of 8. Solve your equations for your particular variable to prove the solution is 8.
4. A business buys magazines for $2.50 each and sells the same magazine for $3.50 each. How many magazines should the business sell in order to profit $125? Create an equation by letting m equal the number of magazines. Solve the equation for m.
II. Research. Research interest rates and find the reasons that interest rates rise and fall. Who sets the interest rates? The discussion should be at least two paragraphs long with at least two sources.
III. You have received an invoice for computer equipment. On the invoice you have ordered 35 servers for a list price of $1200 each. The invoice shows a trade discount series of 3/8/5. Find the net price and the discount of the computer equipment.
IV. The same invoice in part III, gives another option of a total of 16% discount. Are the net prices and the discount for the computer equipment the same? Explain.
1) Let x represent the number of hours enrolled.
If x<= 12, then the tuition is 120
If x > 12, then the tuition is 120 + 10 * (x - 12)
Suppose the a student enrolls in 18 hours, since 18 > 12, the tuition is then
120 + 10 * (18 - 12) = 120 + 60 = 180
2) One of our daily life formula example is the Fahrenheit and Celsius Conversion Formulas
C = (F - 32) * 5/9
where C is degree Celsius and F is degree Fafrenheit. So if we want to find out what is the corresponding degree Celsius for 86 degree Fahrenheit, we would plug F = 86 into the above formua. We get
C = (86 - 32) * 5/9
= 54 * 5/9
= 30 degree Celsius
first equation x + 6 = 14
To solve for x, we minus 6 on both sides of the equation, we get
x + 6 - 6 = 14 - 6
x = 8
second equation 2x = 16
To solve for x, we divide 2 on both sodes of the equation, we get
2x / 2 = 16/2
x = ...
This provides several examples of working with business math applications, including net prices and discount, interest rates, equations, and research.