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Systems of equations — SHSAT practice questions

Practice 92 Systems of equations questions in the app

What this topic is

Systems of equations on the SHSAT Mathematics test covers two-variable linear word problems in which two kinds of items or two groups satisfy a total count plus a second condition on cost, time, or an average.

A student has to set up a pair of equations, or an equivalent substitution, and solve for the quantity the question actually names. The exam tends to present a short story with multiple-choice counts that include both unknowns, so a common trap is reporting the other group or treating an average as if it were a simple total.

Sample questions

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Question 1Mid

At a school event, adult tickets cost 6 dollars each and student tickets cost 4 dollars each. A total of 58 tickets were sold for 276 dollars. How many adult tickets were sold?

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Answer: D — 22

If all 58 tickets had cost 4, the total would have been 232. The actual total was 276, which is 44 more. Each adult ticket adds 2 more than a student ticket, so 44÷2=2244\div2=22 adult tickets were sold.

Question 2Mid

A playlist has 14 training videos. Each short video is 3 minutes long, and each long video is 5 minutes long. The total running time is 54 minutes. How many long videos are in the playlist?

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Answer: B — 6

If there are ll long videos, then there are 14−l14-l short videos. The total time is 5l+3(14−l)=545l+3(14-l)=54. This gives 5l+42−3l=545l+42-3l=54, so 2l=122l=12 and l=6l=6.

Question 3Mid

In a club of 25 students, each student sold either 2 raffle tickets or 5 raffle tickets. The average number of raffle tickets sold per student was 3.2. How many students sold 5 raffle tickets?

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Answer: D — 10

The total number of tickets sold was 25⋅3.2=8025\cdot3.2=80. If xx students sold 5 tickets, then 25−x25-x students sold 2 tickets, so 5x+2(25−x)=805x+2(25-x)=80. This gives 3x+50=803x+50=80, so x=10x=10.

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Practice 92 Systems of equations questions in the app

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