psat-quiz-math

PSAT Math Quiz: Systems of Equations

Content Review

Test your PSAT readiness by taking this PSAT Math quiz!

Question 1

If x and y are both integers such that x + 6 = 17 and y + 9 = 12, what is the value of x + y ?

A. 3

B. 8

C. 11

D. 14

Answer 1

D: Be on the lookout for “sets” of equations that aren’t really systems that require substitution or combination. Here, notice that there is only one variable in each equation, so you can solve for each variable to find that x = 17 – 6 = 11 and y = 12 – 9 = 3. Therefore, the value of is 11 + 3 = 14. (D) is correct.

Question 2

At a certain restaurant, there are 25 tables, and each table has either 2 or 4 chairs. If a total of 86 chairs accompany the 25 tables, how many tables have exactly 4 chairs?

A. 12

B. 15

C. 18

D. 21

Answer 2

C: Create a system of two linear equations where t represents tables with 2 chairs and f represents tables with 4 chairs. The first equation should represent the total number of tables, each with 2 or 4 chairs, or f = 25. The second equation should represent the total number of chairs. Because t represents tables with 2 chairs and f represents tables with 4 chairs, the second equation should be 2t + 4 = 86. Now solve the system using substitution. Solve the first equation for either variable, and substitute the result into the second equation:

f = 25 –> 25 – f

2 (25 -  f) + 4f = 86

50 – 2f + 4f = 86

2= 36

= 18

There are 18 tables with 4 chairs each, (C). This is all the question asks for, so you don’t need to find the value of t.

Question 3

If (xy) is the solution to the system of equations graphed in the figure, what is the value of x + y ?

psat math

A. -2

B. -1

C. 1

D. 4

Answer 3

C: Graphically, the solution to a system of linear equations is the point where the lines intersect. Jot down the coordinates of the point on the graph where the two lines intersect, (01, 2). The question asks for the sum of y, so add the coordinates to get =1 + 2 = 1. Choice (C) is correct.

Question 4

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

Answer 4

C: Translate English into math to write a system of equations with t being the cost of a turkey burger and w equaling the cost of a bottle of water. The first statement is translated as 2tw = $3.25 and the second as 3tw = $4.50. The system is:

2tw = 3.25

3tw = 4.50

You could solve the system using substitution, but combination is quicker in this question because subtracting the first equation from the second eliminates w and you can solve for t:

3t= 4.50

- (2tw = 3.25)

= 1.25

Substitute this value for t in the first equation and solve for w:

2(1.25) + w = 3.25

2.5 + w = 3.25

w = 0.75

Two bottles of water would cost 2 x $0.75 = $1.50, which is (C).

Question 5

Guests at a wedding had two meal choices, chicken or 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. c + v = 725.25, 12.75c + 9.5v = 62

B. c + v = 62, 12.75c + 9.5v = (725.25 / 2)

C. c + v = 62, 12.75c + 9.5v = 725.25

D. c + v = 62, 12.75c + 9.5v = 725.25 x 2

Answer 5

The number of people who ordered chicken plus the number who ordered vegetarian equals the total number of people, 62, so one equation is + v = 62. This means you can eliminate A. Now write the cost equation: Cost per chicken dish (12.75) times number of dishes (c) plus cost per vegetarian dish (9.5) times number of dishes (v) equals the total bill (725.25). The cost equation should be 12.75c + 9.5v = 725.25. Together, these two equations form the system in (C).

 

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