Question 1

Let $$x$$, $$y$$, and $$z$$ represent the capacities of the first, second, and third aircraft, respectively. If the first aircraft has 55 more seats than the second, which equation correctly expresses $$x in $$terms of $$y$$?

Accepted Answer

$$x = y + 55$$

Question 2

If the third aircraft has 65 seats less than twice the seating capacity of the second aircraft, which equation expresses $$z in $$terms of $$y$$?

Accepted Answer

$$z = 2y - 65$$

Question 3

Given the total number of seats is 1850, which equation correctly represents the sum of the three aircrafts' capacities in terms of $$y$$?

Accepted Answer

$$(y + 55) + y + (2y - 65) = 1850$$

Question 4

After combining like terms, what is the simplified equation for the total number of seats?

Accepted Answer

$$4y + 55 - 65 = 1850$$

Question 5

What is the value of $$y$$ after solving $$4y = 1860$$?

Accepted Answer

$$y = 465$$

Question 6

If $$y = 465$$, what is the capacity of the first aircraft ($$x$$)?

Accepted Answer

$$x = 520$$

Question 7

If $$y = 465$$, what is the capacity of the third aircraft ($$z$$)?

Accepted Answer

$$z = 865$$

Question 8

Which of the following best describes the process used to isolate $$y in $$the equation $$4y + 55 - 65 = 1850$$?

Accepted Answer

Combine constants, move them to the right side, then divide both sides by 4

Question 9

Suppose the total number of seats was increased to 2000, but the relationships between the aircrafts remain the same. What would be the new value of $$y$$?

Accepted Answer

$$y = 500$$

Question 10

If the second aircraft had 10 more seats, how would the capacity of the third aircraft change?

Accepted Answer

It would increase by 20 seats

Question 11

Which of the following real-world scenarios could be modeled by the equation $$2y - 65$$?

Accepted Answer

A company’s profit is 65 less than twice its expenses

Question 12

If the total number of seats is 1850 and the first aircraft has 520 seats, what percentage of the total seats does the first aircraft have? (Round to the nearest whole number)

Accepted Answer

28%

Question 13

If the third aircraft’s capacity formula changed to $$z = 3y - 65$$, and $$y = 465$$, what would be the new capacity of the third aircraft?

Accepted Answer

$$z = 1330$$

Question 14

Which step is necessary to check your solution for $$y$$ after solving the equation $$4y = 1860$$?

Accepted Answer

Substitute $$y$$ back into the original expressions for $$x$$ and $$z$$ and verify the total

Question 15

If the first aircraft’s capacity was instead 45 more than the second, what would be the new equation for the total number of seats?

Accepted Answer

$$(y + 45) + y + (2y - 65) = 1850$$

Solving a System of Linear Equations: Aircraft Seating Capacities

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