venomousjz
Answered

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?​

Answer :

Step-by-step 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

[tex]{:}\longrightarrow[/tex][tex]\sf 17x+3x=3000 [/tex]

[tex]{:}\longrightarrow[/tex][tex]\sf 20x=3000 [/tex]

[tex]{:}\longrightarrow[/tex][tex]\sf x={\dfrac {3000}{20}}[/tex]

[tex]{:}\longrightarrow[/tex][tex]\sf x=150 [/tex]

  • 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=

[tex]{:}\longrightarrow[/tex][tex]\sf {\dfrac {3150}{450}}[/tex]

[tex]{:}\longrightarrow[/tex][tex]\sf {\dfrac {1575}{225}}[/tex]

[tex]{:}\longrightarrow[/tex][tex]\sf {\dfrac {315}{45}}[/tex]

[tex]{:}\longrightarrow[/tex][tex]\sf {\dfrac {63}{9}}[/tex]

[tex]{:}\longrightarrow[/tex][tex]\sf {\dfrac {7}{1}}[/tex]

[tex]{:}\longrightarrow[/tex][tex]\sf 7:1 [/tex]

[tex]\therefore[/tex]New ratio of fans to staff is 7:1.

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