Systems of equations — SHSAT practice questions

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Practice 92 Systems of equations questions in the app

What this topic is

A system of equations is a set of equations that share the same unknowns and must be true at the same time.

Many SHSAT problems in this topic are word problems about two kinds of things, such as tickets at different prices or coins of different values, with a total count and a total value given. One equation counts the items and the other adds up their value.

Systems of equations can be solved by substitution or elimination, and a quick check is to imagine every item is the cheaper kind and see how far the total falls short. Averages can also hide a system.

Sample questions

Pick an answer to see whether it is right — nothing is saved, and nothing needs an account.

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?

16✗ Not this one18✗ Not this one20✗ Not this one22✓ Correct

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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 $44 \div 2 = 22$ 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?

4✗ Not this one6✓ Correct8✗ Not this one10✗ Not this one

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Answer: B — 6

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

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?

5✗ Not this one8✗ Not this one9✗ Not this one10✓ Correct

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Answer: D — 10

The total number of tickets sold was $25 \cdot 3.2 = 80$ . If $x$ students sold 5 tickets, then $25 - x$ students sold 2 tickets, so $5 x + 2 (25 - x) = 80$ . This gives $3 x + 50 = 80$ , so $x = 10$ .

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Practice 92 Systems of equations questions in the app

Systems of equations — SHSAT practice questions

What this topic is

Sample questions

More SHSAT topics

Mathematics