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A stadium has 3000 people, including fans and staff. The ratio of fans to staff is 17:3. If another 500 fans arrive then what is the new ratio of fans to staff?​

User Jay Elrod
by
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1 Answer

3 votes

Explanation:

Required Answer:-

Total number of people =3000

Let

the number of fans=17x

The number of staff=3x

  • First we need to find Both numbers of fans and staff

ATQ


{:}\longrightarrow
\sf 17x+3x=3000


{:}\longrightarrow
\sf 20x=3000


{:}\longrightarrow
\sf x={\frac {3000}{20}}


{:}\longrightarrow
\sf x=150

  • Number of fans=17x=17×150=2650
  • Number of staff=3x=3×150=450

____________________________

500 more fans arrived

  • Latest number of fans= 2650+500=3150
  • Latest number of staff=450

Now the new ratio=


{:}\longrightarrow
\sf {\frac {3150}{450}}


{:}\longrightarrow
\sf {\frac {1575}{225}}


{:}\longrightarrow
\sf {\frac {315}{45}}


{:}\longrightarrow
\sf {\frac {63}{9}}


{:}\longrightarrow
\sf {\frac {7}{1}}


{:}\longrightarrow
\sf 7:1


\thereforeNew ratio of fans to staff is 7:1.

User Neil Barnwell
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