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An auditorium is to seat 2,400 people. The building code requires three square feet for each person. How many square meters will that auditorium have?

User Braudy
by
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1 Answer

2 votes
Answer:
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Step-by-step explanation:
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Method 1)

2,400 person (3 ft² / person) = __?__ m² .

The units of "person" ; 'cancel out"; since "person/ person" = 1 ; and 1/1 = 1.

and we have: "2,400 * (3 ft²) = 7, 200 ft² .
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We are ask to find the value, in units of "m² " ;
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→ So; we convert "7, 200 ft² " ; to "m² " ;
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→ Note the conversion: 1 m² = 10.7639 ft² ;
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→ 7, 200 ft² * [ ( 1m²) / ( 10.7639 ft²) ] ;

= [ (7, 200 ) / (10.7639 )] m² ;

= 668.9025353264151469 m² ;

⇒ Round to 668.903 m² .
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Method 2)
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2,400 person (3 ft² / person) = __?__ m² .

Since we want the answer is units of: "m² " ;
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Let us convert: "3 ft² " to units of: "m² " ; and then rewrite the problem.
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Note the conversion: 1 m² = 10.7639 ft² ;
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= [ (7, 200 ) / (10.7639 )] m²

= 668.9025353264151469 m²

⇒ Round to 668.903 m² .
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Method 3)
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2,400 person (3 ft² / person) = __?__ m² .
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Note the conversion: 1 m² = 10.7639 ft² ;
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(2,400 person) * (3 ft² / person) * [ ( 1m²) / ( 10.7639 ft²) ] ;

= { [ (2,400) * (3) * (1) ] / [ 10.7639 ] } m² ;

= { [ (2,400) * (3) ] / [ 10.7639 ] } m² ; {Note: The "1" can be ignored.}.

= [ (7,200) / (10.7639) ] m² ;

= 668.9025353264151469 m² ;

⇒ Round to 668.903 m² .
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User WitoldW
by
7.5k points