Question

1. choose efficient methods for a small music concert, each child in attendance will get a free toy trumpet. five adults are expected for every 2 children. find how many children are expected if there are 15 adults, 25 adults, and 40 adults.
2. which ratios represent pi (π)? select all that apply.

66 : 21
60 : 20
45 : 15
22 : 7
21 : 7

Explanation:

For Question 23:

Step1: Define adult-child ratio

The ratio of adults to children is $5:2$, so for every 5 adults, there are 2 children. Rearranged, the number of children is $\frac{2}{5} \times \text{number of adults}$.

Step2: Calculate for 15 adults

Substitute adult count = 15
$\text{Children} = \frac{2}{5} \times 15 = 6$

Step3: Calculate for 25 adults

Substitute adult count = 25
$\text{Children} = \frac{2}{5} \times 25 = 10$

Step4: Calculate for 40 adults

Substitute adult count = 40
$\text{Children} = \frac{2}{5} \times 40 = 16$

Step1: Simplify each ratio

• $66:21 = \frac{66}{21} = \frac{22}{7} \approx 3.1428$, which matches the approximation of $\pi$
• $60:20 = \frac{60}{20} = 3$, not equal to $\pi$
• $45:15 = \frac{45}{15} = 3$, not equal to $\pi$
• $22:7 = \frac{22}{7} \approx 3.1428$, which is a standard approximation of $\pi$
• $21:7 = \frac{21}{7} = 3$, not equal to $\pi$

Answer:

6 children (for 15 adults), 10 children (for 25 adults), 16 children (for 40 adults)

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For Question 25: