Part 1A jazz concert brought in $172,000172,000 on the sale of 8,4008,400 tickets. If the tickets sold for $ 15$15 and $ 25$25 each, how many of each type of ticket were sold? Part 1The number of $ 15$15 tickets is [input]enter your response here .

Question

Part 1A jazz concert brought in ​$172,000172,000 on the sale of 8,4008,400 tickets. If the tickets sold for $ 15$15 and $ 25$25 ​each, how many of each type of ticket were​ sold? Part 1The number of $ 15$15 tickets is [input]enter your response here .

BlackTom AI · Accepted Answer

Let x = number of $15 tickets sold. Then 8400 − x is the number of $25 tickets.

1. Relevant knowledge points and concepts
- Set up linear equations from totals: one equation for number of tickets, one for total revenue.
- Solve a single-variable linear equation.
- Check solution by substituting back into both count and revenue equations.

2. Complete reasoning process step by step
- Total tickets: x + (8400 − x) = 8400 (this just confirms the partition).
- Revenue equation: 15(x) + 25(8400 − x) = 172000.
- Expand and combine like terms.

3. Calculations with all intermediate steps
15x + 25(8400 − x) = 172000
15x + 25·8400 − 25x = 172000
15x + 210000 − 25x = 172000
(15x − 25x) + 210000 = 172000
−10x + 210000 = 172000
−10x = 172000 − 210000
−10x = −38000
x = (−38000)/(−10) = 3800

Check: $15 tickets = 3800 → revenue 3800·15 = 57,000. $25 tickets = 8400 − 3800 = 4600 → revenue 4600·25 = 115,000. Total revenue = 57,000 + 115,000 = 172,000, and total tickets = 3800 + 4600 = 8400. Both conditions satisfied.

4. Why the correct answer is correct
The algebra directly models the problem: the two ticket types sum to 8400 and their priced contributions sum to the given revenue. Solving the linear equation yields x = 3800, which satisfies both constraints and checks correctly.

5. Why other answers would be incorrect
Common mistakes include sign errors when combining terms (leading to x = 4200 or other wrong values), swapping coefficients, or dividing the total revenue by an average price without accounting for different counts. Any value other than 3800 fails to satisfy both the ticket-count and revenue equations simultaneously.

6. Conclusion
The number of $15 tickets sold is 3800, which matches the provided answer.

Part 1A jazz concert brought in $172,000172,000 on the sale of 8,4008,400 tickets. If the tickets sold for $ 15$15 and $ 25$25 each, how many of each type of ticket were sold? Part 1The number of $ 15$15 tickets is [input]enter your response here .多项填空题

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Part 1A jazz concert brought in ​$172,000172,000 on the sale of 8,4008,400 tickets. If the tickets sold for $ 15$15 and $ 25$25 ​each, how many of each type of ticket were​ sold? Part 1The number of $ 15$15 tickets is [input]enter your response here .多项填空题