# Suppose a news story about the Super Bowl claims "Men outnumbered women in the stadium by a ratio of 9 to 5." Haru thinks that this means there were 14 people in the stadium— 9 men and 5 women. Is this true?

Jul 28, 2018

It could be true. Objectively.

#### Explanation:

The ratio of "9 to 5" means that there are 9 men for every 5 women. If there are 14 people because there are 9 men and 5 women, you have proved the ratio correct.

However, I'm pretty sure that the Super Bowl would have more people in the stadium. So it's more likely that the ratio of men to women is equivalent to a multiple of $\left(9 \text{ men")/(5" women}\right)$

An example: 4,500 men to 2,500 women can be simplified:
$\left(4 , 500 \text{ men")/(2,500" women")=(45" men")/(25" women")=(9" men")/(5" women}\right)$

Jul 28, 2018

It is not true.

#### Explanation:

The average attendance of a Super Bowl game over the past $47$ years is $77 , 987$ spectators.
https://www.sportingcharts.com/articles/nfl/super-bowl-attendance-by-the-numbers.aspx

The ratio of men to women of $9 : 5$ just means that for every 9 males, there will be 5 females.

If we divide the total number of spectators by $5$, we can calculate the number of males, and if we divide the total number by $9$, we can calculate the number of females.

no. of females$=$$\frac{77987}{9} = 8665$ $\text{females}$

no. of males $\frac{77987}{5} = 15597$ $\text{males}$

$\frac{9}{5} = 1.8$

$\frac{15597}{8665} = 1.8$