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Solving Systems of Linear Equations, Cheat Sheet of Engineering

Adventist University of Central AfricaEngineering

A series of assignments focused on evaluating percentages, solving linear equations, and setting up and solving systems of linear equations. The assignments cover a range of topics, including converting percentages to decimals, solving single and multi-variable linear equations, and using systems of equations to solve real-world problems involving product production, rental costs, and pricing of goods. A comprehensive set of practice problems and solutions, making it a valuable resource for students studying linear algebra, applied mathematics, or business-related subjects. By working through these assignments, students can develop their problem-solving skills, strengthen their understanding of linear equations, and apply these concepts to practical scenarios.

Typology: Cheat Sheet

2021/2022

Uploaded on 06/21/2022

teta-doriane
teta-doriane 🇷🇼

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ASSIGNMENT 1 (total 30 marks)
1. Evaluate each of the following (3 marks).
2. Change each of the following percents into a decimal (3 marks).
a. 175%
b. 38%
c. 0.5%
3. Solve each of the following equations (3 marks).
4. A machine requires three hours to make a unit of Product A and five
hours to make a unit of Product B. The machine operated for 395
hours, producing a total of 95 units. How many units of Product B were
produced? (3 marks)
5. Departments A, B, and C occupy floor space of 40 m2, 80 m2, and 300
m2, respectively. If the total rental for the space is $25 200 per month,
how much rent should Department B pay? (3 marks)
6. Set up a system of equations to solve each of the following problems.
(a)6A tire store sold two types of tires, a sports tire and an all-season
tire. The sum of six times the sports tire and five times the all-season
tire is 93, and the difference between three-quarters of the sports tire
and two-thirds of the all-season tires is zero. For the store manager, find
the number of each type of tire sold in one day (3 marks).
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ASSIGNMENT 1 (total 30 marks)

  1. Evaluate each of the following (3 marks).
  2. Change each of the following percents into a decimal (3 marks). a. 175%

b. 38%

c. 0.5%

  1. Solve each of the following equations (3 marks).
  2. A machine requires three hours to make a unit of Product A and five hours to make a unit of Product B. The machine operated for 395 hours, producing a total of 95 units. How many units of Product B were produced? (3 marks)
  3. Departments A, B, and C occupy floor space of 40 m^2 , 80 m^2 , and 300 m^2 , respectively. If the total rental for the space is $25 200 per month, how much rent should Department B pay? (3 marks)
  4. Set up a system of equations to solve each of the following problems. (a) A tire store sold two types of tires, a sports tire and an all-season tire. The sum of six times the sports tire and five times the all-season tire is 93, and the difference between three-quarters of the sports tire and two-thirds of the all-season tires is zero. For the store manager, find the number of each type of tire sold in one day (3 marks).

(b) The college theatre collected $1300 from the sale of 450 tickets. If the tickets were sold for $2.50 and $3.50, how many tickets were sold at each price? (3 marks) (c) A jacket and two pairs of pants together cost $175. The jacket is valued at three times the price of one pair of pants. What is the value of the jacket? (3 marks) (d) Three cases of white Bordeaux and five cases of red Bordeaux together cost $438. Each case of red Bordeaux costs $6 less than twice the cost of a case of white Bordeaux. Determine the cost of a case of each type. (3 marks)

  1. Graph each of the following (3 marks)

(a) 2 x−y= 6

(b) 3 x+ 4 y= 0

(c) 5 x+ 2 y= 10

ANSWER KEY

  1. (a)

(a) Let x represent the number of sports tires sold, y the number of all-season tires sold. (1) (2) 9 x – 8 y = 0 (3) 45 x – 40 y = 0 48 x + 40 y = 744 Add: In (3) 8 sports tires were sold, 9 all-season tires were sold. (b) Let the number of $2.50-tickets be x and that of $3.50-tickets be y. (1) (2) To eliminate x Subtract: (c) Let the price of a jacket be $ x and that of a pair of pants be $ y. (1) (2)

Substitute (2) in (1) (d) Let the cost of a case of white bordeaux be $ x and that of a case of red bordeaux be $ y. (1) (2) Substitute (2) in (1)

(a) x 3 0 5 y 0  6 4 (b) x 0  4 4 y 0 3  3