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There are 60 players on a high school football team. The ratio of juniors and seniors to freshmen and sophmores on the team is 2:3. The ratio of juniors to seniors on the team is 1:2. How many juniors are on the team? How many seniors?


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rickyboedeker
You know that the ratio of J&S to F&So is 2:3. You need two numbers that have that same ratio to total 60 players.  When you multiply both numbers by 12, you have a ratio of 2:3 but the number of players is 24 to 36.  Thus, the total players is 60.  When looking at the ratio of Juniors to Seniors, the ratio remains 1:2, but must total 24 players.  Dividing the total players by 3, you can find where 1 part of the players equals 2 parts of the others.  Keeping that same ratio in mind, you are able to calculate that the ratio of Juniors to Seniors is 8:16 but when reduced, still remains a 1:2 ratio.

Answer with Step-by-step explanation:

There are 60 players on a high school football team.

The ratio of juniors and seniors to freshmen and sophomores on the team is 2:3.

i.e. number of juniors and seniors are:

[tex]\dfrac{2}{2+3}\times 60[/tex]

=24

The ratio of juniors to seniors on the team is 1:2.

i.e. number of juniors are:

[tex]\dfrac{1}{1+2}\times 24[/tex]

=8

and number of seniors are:

[tex]\dfrac{2}{1+2}\times 24[/tex]

=16

Hence, Number of juniors=8

and number of seniors=16

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