# Examples of Real World Applications in Business Math

1) How can you solve for an equation of a line given the following.

A. One point and the slope

B. Two points

C. Slope

2) When graphing a linear inequality. How do you know if the inequality represents the area above or below the line? How do you know if it also represents the points on the line?

3) Why is it true that any two points satisfying a linear equation will give you the same graph for the line represented by the equation?

4) How do you interpret the slope and y intercept in a real world case?

5) When solving a linear inequality, why do you always solve for y?

6) Give an example of a function that you use in your profession.

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#### Solution Preview

1) How can you solve for an equation of a line given the following:

A. One point and the slope

Remember, a line has the equation y = mx + c.

m is the slope and c is the y-intercept.

If you're given one point, then you have the x and y coordinates, since a point is always the form (x,y). If you have been given the slope as well, then you have m. Therefore, you can plug everything into the basic equation for a straight line and solve for c.

B. Two points

From two points, you can calculate the slope. To solve for the slope, remember that the slope is the change of y divided by the change of x. Now, that we have the slope, you can solve the equation the same way as in A above.

C. Slope

In this case, all we can determine is the slope of the line. We have no idea where the line is on the graph. We just know that it has a specific slope. We cannot solve the ...

#### Solution Summary

In simple, easy to understand language, this solution provide detailed solutions to each of these questions regarding the application of simple mathematics in business applications. When explained carefully, it's really not that difficult!

Real world math inquiries are made and solved using fractions, ratios, measurement conversions, and fraction operations.

As a new graduate from the police academy, you have to qualify your weapon. Qualifying means going to the gun range with your assigned Glock .40 caliber with a 15-round magazine and hitting the target four out of five times.

Write the smallest fraction that represents successfully qualifying.

If you have two magazines, how many misses would you be allowed to still qualify?

After successfully qualifying, you have been called to a murder scene. The sergeant has requested that you find the measurements of the location of the murder weapon at the crime scene so that they can be reproduced in drawings by the police sketch artist.

You have discovered the murder weapon located 2 1/2 feet from the north wall and 6 1/4 feet from the east wall. However, the sketch artist has informed you that his drawing program is scaled to inches and not feet.

Answer the following questions to write out your report for the sergeant with the needed measurements for the sketch artist:

How many inches from the north wall is the murder weapon? How many inches from the east wall? (Hint: Conversion units: 1 ft. = 12 in.)

Explain once you have the conversions in inches how to convert back to feet. Explain in detail.

Business

In business, it is always important to get the best deal. Your employer has asked you to research prices of new tires for the company's truck fleet. Truck Zone has a special on tires, with a normal sales price of $85 per tire. However, with this sale, you can purchase two tires for $157.50.

How much does each tire cost at the sales price of $157.50 for buying two tires at a time?

How much can you save per tire and overall by purchasing two tires at the sale price

How did fractions come into play for calculating the price of two tires?

After saving money for your company by purchasing the tires on sale, the company had leftover profits of $2,875 for the first week of business. The company plans to divide the profits as follows:

1/4 of the profits will go in your savings account.

3/5 of the profits will go back into the company.

The first week's employee wages paid out of the profits are $600.

Answer the following questions based on the division of the profits:

How much in dollars goes into the savings account?

How much in dollars goes back into the company?

After the division of the profits for the savings and back into the company, was there enough left over to pay the first week's wages?

Medical

Accuracy in measuring medicine is crucial, and incorrect measurements could result in devastating consequences. Thus, learning how to convert between various measurements is important for anyone working in the medical field. There are various measurements used in health care facilities, such as the unit of one drop from a dropper (abbreviated as gtt.); 60 drops, or 60 gtts., is equal to 1 teaspoon (tsp.).

In a prescription cough syrup, the dosage calls for 2 1/2 teaspoons every 6 hours. The patient is given a dropper in the prescription and therefore needs to know how many gtts. are in the 2 1/2 teaspoons. How many gtts. are in 2 1/2 tsps.?

In a prescription cough syrup, the dosage calls for 140 drops. How many teaspoons should the patient be given in an exact fractional amount?

Real Life

One important use of fractions is being able to divide recipes into parts, that is, smaller sizes. For example, you may have found a recipe that you like but it serves 25 people and you only have 4 to serve in your family.

1) Find a favorite recipe with at least 3 ingredients.

2) List the measurements and ingredients of the original recipe.

3) You wish to use the original recipe but want to cut it down by two-thirds. Show the calculations for modifying the recipe. Be sure to reduce all fractions.

4) Did you come up with any values that are not typical measuring cup sizes? If so, how could you get the measurement?