Mat101 SLP 2 Answer Template Name: Date: Instructor: Use Thi

Mat101 Slp 2 Answer Template Name: Date: Instructor: 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. Write the final answer in the terms being asked such as dollars/cents, degrees, tickets, etc.

This assignment involves solving various algebraic problems, including creating and solving equations and inequalities, working with word problems, and understanding absolute value equations. The problems require setting up mathematical models based on written scenarios and then solving for the required variables, ensuring proper application of mathematical principles and clarity in presentation.

Paper For Above instruction

The assignment encompasses multiple mathematical problems that test foundational algebra skills and their application to real-world contexts. It begins with word problems involving profit calculations, selling prices, and expenses. Then, it transitions into geometric problems such as calculating the dimensions of a pool based on perimeter constraints, and finally, it includes tax calculations, average score requirements, fencing, leasing decisions, and calorie burning estimates. Additionally, the assignment addresses solving absolute value equations and inequalities, graphing solutions, and highlighting when and why the inequality sign must be reversed during the solution process.

In the first problem, the goal is to determine how many magazines a firm must sell to achieve a net profit of $550, given costs and selling prices. An equation is formed based on profit calculations: revenue minus costs equals profit. The equation is set up as 550 = (2.50x) - (1.75x) - 40, where x is the number of magazines. Simplifying, the combined revenue per magazine is calculated, and then the equation is solved for x, giving x = 787 units, meaning they need to sell 787 magazines to reach their profit goal.

The second problem involves splitting a total amount of $900 received from the sale of a computer and software. Using the relationship that the computer sold for three times the software, the equation 3x + x = 900 is created, where x is the software's selling price. Simplifying yields 4x = 900, so x = 225. Consequently, the computer's price is 3 x 225 = 675, and the software's price is 225, which matches the total sale amount.

The third problem involves a rectangular pool with a known perimeter of 64 feet, where the width is x and the length is x - 4. The perimeter formula P = 2(length + width) leads to the equation 64 = 2((x - 4) + x). Simplifying this, 64 = 2(2x - 4), and further distributing gives 64 = 4x - 8. Solving for x results in 4x = 72, so x = 18. The width of the pool is 18 feet, and the length is x - 4 = 14 feet.

The fourth problem calculates the total purchase amount given the sales tax. The tax amount is $9.33, which is 6% of the purchase price. The equation is set as 0.06 * total = 9.33, with the solution total = 9.33 / 0.06, resulting in a total purchase of approximately $155.50.

The fifth problem requires calculating the minimum final exam score needed for Mike to achieve at least a 75% average in a class with five equally weighted exams. The scores on the first four exams are provided, and the total of these scores is summed. The inequality (64 + 86 + 71 + 90 + x) / 5 ≥ 75 is used, leading to solving for x to find the minimum score required on the final exam, which works out to be at least 64%.

The sixth problem involves determining the maximum width of a fence with a length constraint. With a total available wood of 330 feet and length no more than 90 feet, an inequality is set based on the perimeter formula (2l + 2w ≤ 330). By substituting l = 90 and solving for w, the maximum width is approximately 82.5 feet.

In the seventh problem, a leasing scenario is evaluated to decide if leasing a copy machine is cost-effective given the estimated number of copies (10,500). The monthly costs, including leasing, copying per sheet, and paper costs, are compared through an inequality to see if the total cost remains within the budget of $750. Calculating the total monthly expense reveals whether leasing is a feasible option based on the total number of copies.

The eighth problem involves a budget for a surprise party. The total planned expenditure per person includes food and drinks at $20 each, plus a $35 cleanup fee. An inequality is used to determine the maximum number of guests, involving the total cost not exceeding the $350 budget, and solving for the number of guests yields the maximum count.

The ninth problem estimates the minimum duration Sally needs to walk to burn at least 250 calories, given a burn rate of 4.6 calories per minute. An inequality is set up as 4.6 x ≥ 250, and solving for x determines the fewest minutes she must walk, rounded appropriately to verify accuracy.

Finally, the tenth problem discusses the rule for reversing the sign when solving inequalities. The sign must be flipped whenever both sides of the inequality are multiplied or divided by a negative number, ensuring the inequality direction remains valid.

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