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Subject Test Math 1

Question 5 of 32

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SAT Subject Test

Tickets for a show cost $ 3 or $ 5. If 50 tickets were sold for a total of $ 230, how many tickets were sold for $ 3?

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10

Correct Answer: 
Yes

20

Correct Answer: 
No

25

Correct Answer: 
No

30

Correct Answer: 
No

40

Correct Answer: 
No

One way to solve this problem is to set up an equation using one variable. Let n represent the number of $ 3 tickets sold; then 50 invisible times minus n represents the number of $ 5 tickets sold.


3 n plus 5 left parenthesis 50 minus n right parenthesis equals 230

3 n plus 250 minus 5 n equals 230

20 equals 2 n

10 equals n

There were 10 $ 3 tickets sold.

Simultaneous equations can also be set up to solve the problem. Let n represent the number of $ 3 tickets sold and p represent the number of $ 5 tickets sold.


n plus p equals 50
3 n plus 5 p equals 230

Another way to solve this problem is to realize that each of the tickets costs at least $ 3. At $ 3 each, a total of $ 150 would be collected from selling all 50 of the tickets. Since the remaining $ 80 was the extra $ 2 collected from each of the $ 5 tickets, 40 of the $ 5 tickets were sold. This implies that 10 of the $ 3 tickets were sold.

Question Difficulty: 
medium