Tickets for the school play were priced at ₦520.00 each for adults and ₦250.00 each for kids. How many kids'…

Analysis

To solve this problem, we need to translate the word problem into algebraic equations. We are looking for the number of kids' tickets sold, given the prices, the total revenue, and the relationship between the number of adult and kids' tickets.

Concept

We can use a system of linear equations. Let:

• $x$ = the number of kids' tickets sold.
• $5x$ = the number of adult tickets sold (since there were 5 times as many adult tickets as kids' tickets).

The total revenue is the sum of (price of adult tickets × number of adult tickets) and (price of kids' tickets × number of kids' tickets).

Step-by-Step Solution

1. Set up the equation: • Price of adult ticket = ₦520 • Price of kids' ticket = ₦250 • Total revenue = ₦171,000

The equation is: $(520 \times 5x) + (250 \times x) = 171,000$

2. Simplify the equation: • $2600x + 250x = 171,000$ • $2850x = 171,000$

3. Solve for $x$: • $x = \frac{171,000}{2850}$ • $x = \frac{17,100}{285}$ • $x = 60$

4. Verify: • If kids' tickets ($x$) = 60, then adult tickets ($5x$) = 300. • Revenue from kids = $60 \times 250 = 15,000$ • Revenue from adults = $300 \times 520 = 156,000$ • Total = $15,000 + 156,000 = 171,000$. The calculation is correct.

Conclusion

The number of kids' tickets sold is 60. This matches option D.

Exam Tip

When you see "5 times as many X as Y," always write it as $X = 5Y$. A common mistake is to write $5X = Y$, which flips the ratio. Always do a quick mental check: if there are more adults, the adult count should be the larger number!