PSAT/NMSQT Prep 2022 - Eggert M.D., Strelka A. 2022

How much have you learned?
Systems of linear equations
The heart of algebra

Directions: For testlike practice, give yourself 15 minutes to complete this question set. Be sure to study the explanations, even for questions you answered correctly. They can be found at the end of this chapter.

17. What is the value of y − x, if 6x − 4y = 8 and 5y − 7x = 12?

A. −8

B.4

C.12

D. 20

18. A bed costs $40 less than three times the cost of a couch. If the bed and couch together cost $700, how much more does the bed cost than the couch?

A. $185

B.$225

C.$330

D. $515

19. If k is a constant and the above system of linear equations has infinitely many solutions, what is the value of k?

A. −8

B.−4

C.−2

D. −1

20. What is the value of |a − b| if a and b are constants and the above system of equations has no solution?

A. −13

B.−8

C.8

D. 13

21. If and −4y − x = 12, what is of y?

22. A local airport has separate fees for commercial airliners and private planes. Commercial flights are charged a landing fee of $281 per flight and private planes are charged a landing fee of $31 per flight. On a given day, a total of 312 planes landed at the airport and $47,848 in landing fees was collected. Solving which of the following systems of equations yields the number of commercial airliners, c, and the number of private planes, p, that landed at the airport on the day in question?

A.

B.

C.

D.

23. At a certain coffee store, the small bag of beans costs $2.50 and the large bag of beans costs $15. If the store sold 27 small and large bags of beans and had $155 in revenue in one week, how many small bags and large bags of beans were sold?

A. 20 small bags, 7 large bags

B.7 small bags, 20 large bags

C.8 small bags, 19 large bags

D. 20 small bags, 9 large bags

24. If (x, y) is a solution to the system of equations shown above, then what is the value of x − y ?

A.

B.

C.

D.

25. Guests at a wedding had two meal choices, chicken and vegetarian. The catering company charges $12.75 for each chicken dish and $9.50 for each vegetarian dish. If 62 people attended the wedding and the catering bill was $725.25, which of the following systems of equations could be used to find the number of people who ordered chicken, c, and the number of people who ordered vegetarian, v, assuming everyone ordered a meal?

A.

B.

C.

D.

26. Two turkey burgers and a bottle of water cost $3.25. If three turkey burgers and a bottle of water cost $4.50, what is the cost of two bottles of water?

A. $0.75

B.$1.25

C.$1.50

D. $3.00