Math 101 Module 2 slp (Math Problem Sample)

[MAT101 SLP 2 Answer Template
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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.
Write the final answer in the terms being asked such as dollars/cents, degrees, tickets, etc.
1. A firm pays $1.75 for each copy of a magazine and sells each one for $2.50. There is a fixed monthly cost of $40 for printing the publication. If the firm wants to make $550 dollars next month, how many magazines do they have to sell? Write and solve an equation that represents this scenario.
Equation:
The question requires the estimation of a profit function that is given by: Profit=Total revenue-total costs.
Let’s say the number of magazines is x where profit shall be represented as follows:
P=x.$2.5-(x.1.75+$40).
Calculations:
Profit in this context equals to $550 where $550=2.5x-1.75x-$40.
Collecting of like terms and putting them on one side of the equation we get:
$550+$40=$2.5x-$1.75x
$590=$0.75x
X=590/0.75
X=786.67
The number of magazines sold is 787.
Answer: 787 magazines.
2. Martin sold his computer and software for $900, receiving three times as much for the computer than the software. What was the selling price of the computer and the software? Write and solve an equation.
Equation:
Let the computer be denoted as C while the Software is denoted as S. The total sales revenue from the two commodities is $900 where the formula to get the individual sales revenue is as follows:
C received 3 times more than S in terms of revenue which translates into 3x and x respectively. The equation becomes:
3x+x=$900
Calculations:
3x+x=$900 can be computed as follows:
Addition of like terms is firstly effected where 3x+x=4x
So, 4x=$900 where x=900/4= $225
The revenue derived from the sale of the computer is 3x where x=225 thus leading to 3.225=$675 while the revenue derived from the software is x which is $225.
Answer: computer= $675 software=$225.
3. The perimeter of a pool is 64 feet and has a width of x and a length of x-4. Write an equation and find both the width and length of the pool.
Equation:
Perimeter refers to an area surrounding an object where the length and width are both considered in the estimation.
P=2(L+W)
P=2(X-4+X)
Calculations:
Perimeter in this context equals to 64 feet
Where 64=2(x-4+x)
64=2x-8+2x
Collecting of the like terms and putting them to one side of the equation leads to:
64+8=2x+2x
72=4x
X=72/4
X=18
Width =x=18 feet while the length =x-4 =18-4 which is 14
Answer: width= 18 length=_14
4. The tax on a purchase was $9.33. If the sales tax rate is 6%, how much was the purchase? Write and solve an equation.
Equation:
(100%.$9.33)/6%
Calculations:
$933/6= $155.5
Answer: $155.5
5. Mike needs at least a 75% average to pass his math course. The class contains 5 exams that are equally weighted. If he scored a 64%, 86%, 71%, and 90% on the first 4 tests, what score does he need on the final test to earn at least a 75% in the class. Write and solve an inequality.
Inequality:
Let’s say that the score for the fifth exam was x where the average shall be represented by the equation below:
(64+86+71+90+x)/5=75
Calculations:
(311+x)/5=75
311+x=375
X=375-311
X=64
Answer: 64%.
6. The Parker’s are installing a wooden fence in their backyard. They have 330 feet of wood. The length can be no more than 90 feet. Write and solve an inequality to find the maximum width of the fence.
Inequality:
P=2(L+W)
The perimeter of the fence should be organized in such a manner where it does not exceed 330 feet. Let the width be x
2(90+x) ≤330
180+2x≤330
2x≤330-180
2x≤150
x≤75
Calculations:
Answer: _Maximum width is 75 feet.
7. Paula is an office manager for ABC Advertising. She has been tasked with finding a copy machine that falls within a budget of $750 per month. She finds a company that will lease the machine for $275 a month. Each copy costs 4 and a ream of 500 sheets of paper costs $5.00. If she estimates that they will make 10,500 copies per month, is leasing this machine a good choice? Write and solve an inequality and explain your reasoning.
Inequality:
Let the number of copies be expre...