Question 1

A rectangular soccer field has a perimeter of 320 yards. The length is 40 yards more than the width. What is the width of the field?

Accepted Answer

$$w = 60$$

Question 2

Given the same soccer field problem: Perimeter is 320 yards, and length is 40 yards more than width. What is the length of the field?

Accepted Answer

$$l = 100$$

Question 3

Which of the following systems of equations correctly models the soccer field problem where the perimeter is 320 yards and the length is 40 yards more than the width?

Accepted Answer

$$2l + 2w = 320$$ and $$l = w + 40$$

Question 4

If you have two football tickets and one basketball ticket costing a total of $$283.42, and one football ticket and two basketball tickets costing 219.95$$, what is the price of one basketball ticket?

Accepted Answer

$$b = 52.16$$

Question 5

In the ticket problem, what is the price of one football ticket?

Accepted Answer

$$f = 115.63$$

Question 6

Which method is used to solve the system of equations in the soccer field example?

Accepted Answer

Substitution

Question 7

Which method is used to solve the system of equations in the ticket price example?

Accepted Answer

Elimination

Question 8

If a rectangular field has a perimeter of $$P$$ and the length is $$k$$ more than the width, which system of equations models this situation?

Accepted Answer

$$2l + 2w = P$$ and $$l = w + k$$

Question 9

A student is solving a system of equations for a real-world problem. What is the correct order of steps according to the notes?

Accepted Answer

Assign variables, write a system, solve the system

Question 10

Suppose you are given the following system: $$2x + y = 283.42$$ and $$x + 2y = 219.95. $$What is the value of $$x$$?

Accepted Answer

$$x = 115.63$$

Question 11

If the length of a rectangle is 40 yards more than the width and the perimeter is 320 yards, which equation would you use to express the perimeter in terms of width only?

Accepted Answer

$$2(w + 40) + 2w = 320$$

Question 12

A real-world application requires you to find the dimensions of a rectangular lot with a fixed perimeter and a known relationship between length and width. Which algebraic concept is most appropriate to use?

Accepted Answer

Systems of linear equations

Question 13

If you solve the system $$2f + b = 283.42$$ and $$f + 2b = 219.95 by $$elimination, what is the first step?

Accepted Answer

Multiply the second equation by 2

Question 14

Which of the following best describes the process of solving an applied problem using a system of equations?

Accepted Answer

Identify what is given and what is to be found, assign variables, write a system, solve the system

Question 15

A rectangular garden has a perimeter of 320 feet. If the length is 40 feet more than the width, what are the dimensions of the garden?

Accepted Answer

Length = 100 ft, Width = 60 ft

Question 16

If the solution to a system of equations is $$(x, y) = (115.63, 52.16)$$, which of the following systems could this solution correspond to?

Accepted Answer

$$2x + y = 283.42$$ and $$x + 2y = 219.95$$

Question 17

A rectangular field has a length that is 40 meters more than its width. If the perimeter is 320 meters, what equation would you use to solve for the width?

Accepted Answer

$$2(w + 40) + 2w = 320$$

Question 18

Which of the following is NOT a step in solving an applied problem using a system of equations, according to the notes?

Accepted Answer

Guessing the answer

Applications of Systems of Linear Equations: Applied & Money Problems 3.3

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