Question

23
there are 84 boys and 72 girls in the sixth grade. jerod says that the ratio of girls to boys is 6:7. is he correct? why or why not?
24
an airline runs 156 domestic flights and 34 international flights each day from a particular airport. a passenger states that the ratio is 39 to 9. is the passenger correct? why or why not?

Explanation:

Problem 23

Step 1: Identify the given values

We have 72 girls and 84 boys. We need to find the ratio of girls to boys.

Step 2: Write the ratio of girls to boys

The ratio of girls to boys is \( \frac{72}{84} \).

Step 3: Simplify the ratio

To simplify \( \frac{72}{84} \), we find the greatest common divisor (GCD) of 72 and 84. The GCD of 72 and 84 is 12. Divide both the numerator and the denominator by 12: \( \frac{72 \div 12}{84 \div 12} = \frac{6}{7} \). So the ratio of girls to boys is \( 6:7 \).

Step 1: Identify the given values

We have 156 domestic flights and 34 international flights. We need to check if the ratio of domestic to international flights is \( 39:9 \).

Step 2: Write the ratio of domestic to international flights

The ratio of domestic to international flights is \( \frac{156}{34} \).

Step 3: Simplify the ratio

First, find the GCD of 156 and 34. The GCD of 156 and 34 is 2. Divide both the numerator and the denominator by 2: \( \frac{156 \div 2}{34 \div 2} = \frac{78}{17} \). Now, let's simplify \( 39:9 \) (or \( \frac{39}{9} \)). The GCD of 39 and 9 is 3. Divide both by 3: \( \frac{39 \div 3}{9 \div 3} = \frac{13}{3} \). Since \( \frac{78}{17}
eq \frac{13}{3} \) (cross - multiply: \( 78\times3 = 234 \) and \( 17\times13 = 221 \), and \( 234
eq221 \)), the ratio \( 39:9 \) is incorrect.

Answer:

Jerod is correct because when we simplify the ratio of the number of girls (72) to the number of boys (84), we get \( 6:7 \).

Problem 24