Question

Are any of these answers correct?

Of all video game players, 1/8 are men over age 50 and 2/5 are women. what fraction represents men younger than 50 years old?

13/40 are men under 50

21/40 are men under 50

17/40 are men under 50

23/40 are men under 50

please helm me out!​

Answer 1

19/40

Explanation:

⅛ over 50

⅖ women

5 x 8 = 40

8 x 2 = 16

1 x 5 = 5

16 + 5 = 21

40 - 21 = 19

19/40

Answer 2

19/40 are men under 50

Explanation:

Given:

• 2/5 of all video game players are women
• 1/8 of all video game players are men

`\begin{aligned}\textsf{Men under 50 yrs old} & = \textsf{total proportion of men} - \textsf{proportion of men over 50}\\\\& = \left(1-(2)/(5)\right)-(1)/(8)\\\\& = (3)/(5)-(1)/(8)\\\\& = (3 \cdot 8)/(5 \cdot 8)-(1 \cdot 5)/(8 \cdot 5)\\\\& = (24)/(40)-(5)/(40)\\\\& = (19)/(40)\end{aligned}`

To check this, let's assign a number to the total number of players and use this to help us calculate the proportion of players who are men under 50 years old.

Let the total number of video game players be 400.

If 2/5 of all video game players are women, then the proportion of all video game players that are men is: 1 - 2/5 = 3/5

⇒ total number of men = 3/5 of 400 = 3/5 × 400 = 240

If 1/8 of all video game players are men over 50 years old then:

⇒ number of men over 50 yrs old = 1/8 × 400 = 50

Therefore:

⇒ number of men under 50 yrs old = 240 - 50 = 190

Finally, the fraction of men under 50 years old from all video game players is the number of men under 50 divided by the total number of men.

⇒ men under 50 years old = 190/400 = 19/40