# MAT101 Case: Expressions and Equations (Math Problem Sample)

Complete the following problems using the SLP 1 Answer Template.

Write the final answer in the terms being asked such as dollars/cents, degrees, tickets, etc.

Companies often sell products at or below cost in order to draw in and retain customers. Redman Manufacturers is tracking 5 items from last month’s sales. On item #1 they make $15; item #2 loses $4; item #3 makes $9; item #4 loses $6; and item #5 makes $12. Last month’s sales are as follows:

Item #1: 90 units sold

Item #2: 103 units sold

Item #3: 78 units sold

Item #4: 45 units sold

Item #5: 164 units sold

Write, simplify, and, calculate the profit or loss for the month.

When principal (P) is invested at a rate of (R) over a period of time (T) in years, simple interest (I) is earned. The simple interest is calculated by multiplying the principal, rate, and time. Write an equation to represent this scenario.

Using the formula above, calculate the interest earned for an investment of $15,000 at a rate of 5% over 10 years.

The perimeter of a rectangle is P=2L+2W where L is the length and W is the width. Find the perimeter when L=15 and W=25. Show your work.

The formula for a triangle is A= 1/2bh. If the area of a triangle is 36 and the height is 9, what is the base?

The formula F= 9/5C+32 relates Celsius and Fahrenheit temperature. If the current temperature is -20°C, what is the temperature in Fahrenheit?

A triangle has sides measuring x+7, 2x+3, and 5x-6. Write and simplify an expression that represents the perimeter of the triangle.

Floral Solutions is calculating their profits for the previous month. Profit is determined by revenue minus the cost. The cost of producing floral arrangements is represented by the equation C= 18+35x and the revenue is represented by the equation R=80x+12.

Find the simplified expression that represents the profit.

Find the profit made when 110 arrangements are sold.

Jamie sold her house for x dollars. The real estate agent received a 5% commission and Jamie received $197,125. Write and solve an equation to determine the selling price of the house.

Dan works on commission and earns 4% on all of his sales. In month 1, he sold $25,000; month 2 was $17,000; and month 3 was $34,000. 18% of his total earnings are taken out for taxes. Calculate the total net (after taxes) pay Dan earned over the 3 months. Write and simplify an expression that represents this scenario.

MAT101 Case 1 Answer Template

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I affirm that this assignment contains all original work. I am familiar with Trident University’s Academic Integrity policy located in the Trident HYPERLINK "/catalog-handbook"Policy Handbook. I affirm that I have not engaged in direct duplication, copy/pasting, sharing assignments, collaboration with others, contract cheating and/or obtaining answers online, paraphrasing, or submitting/facilitating the submission of prior work. Work found to be unoriginal and in violation of this policy is subject to consequences such as a failing grade on the assignment, a failing grade in the course, and/or elevated academic sanctions. My name below affirms that the assignment was completed individually, and all work presented is my own.

Use this template to insert your answers for the assignment. Please use one of the four methods for showing your work (EE, Math Type,ALT keys, or neatly typed). Remember that your work should be clear and legible.

Problems need to include all required steps and answer(s) for full credit. All answers need to be reduced to lowest terms where possible.

1. Identify the coefficients, variable terms (with exponents), and constants in the following expression.

2x3+5y2-3z+1

Coefficients: 2, 5, and -3.

Variable terms: x, y, and z

Constants: 1 is the only constant

2. Identify the coefficients, variable terms (with exponents), and constants in the following expression.

4z5-8x2-6

Coefficients: 4 and 8

Variable terms: x and z

Constants: -6

3. Combine like terms in the following expression.(Hint: You can color code the like terms.)

8x2+3x+9+7x-2+y

Calculations:

8x2 and -x2 9are like terms, while 3x and 7x are also a set of like terms.

The like terms can be combined as illustrated below:

8x2-x2+3x7x+y+9 +-2

7x2+10x+y+7

Answer: 7x2+10x+y+7

4. Distribute and combine like terms in the following expression.

3(6y2-9+7x-2x2-3x-6)

Calculations:

To expand the above equation, it is essential to first of all multiply each aspect within the bracket by 3 as follows:

3(6y2-9+7x-2x2-3x-6)

3.6y2-3.9+3.7x-3.2x2—3.3x-3.6

18y2-27+21x-6x2-9x-18

Collecting of like terms leads to:

18y2-6x2-27-18+21x-9x

12 y2-48+12x

12 y2+12x-48

Answer: 12 y2+12x-48

5. Write and simplify an expression that applies the distributive property. Include at least 3 different terms.

Calculations:

An example of an expression that applies the distributive property and has at least 3 different terms is 5(4x-3y2-9w+7y2+1)

The first step involves expanding the expression and multiplying the like terms as follows:

5.4x-5. 3y2-5.9w+5.7y2+5.1

20x-15 y2-45w+35y2+5

Collecting like terms we obtain:

20x-15 y2+35y2-45w+5

This can be simplified to:

20x-20 y2-45w+5

Answer: 20x-20 y2-45w+5

6. Simplify the expression using the order of operations. (Note: * stands for multiplication)

(6*2-4) – 3(8-5) * 7

2

Calculations:

The order of operations is quite useful in solving various equations since it shows the order in which the equations have to solve at any given instance. Solutions have ...

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