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At a youth camp, 37 youths participated in at least one of canoeing and archery. If 24 went canoeing and 22 did archery, how many participated in both of these activities?

Sagot :

sordum26

Answer:

19 youths participated in both of these activities

The number of youths participated in both canoeing and archery is equal to [tex]9.[/tex]

What is a number?

" Number is defined as the count representing for a given quantity."

Formula used,

[tex]n(A\cup B) = n(A) + n(B) -n(A\cap B)[/tex]

According to the question,

Given,

'A' represents the youth participating in canoeing

'B'  represents the youth participating in archery

Total number of youths in a youth camp [tex]'n(A\cup B)' = 37[/tex]

Number of youth went for canoeing [tex]'n(A)' =24[/tex]

Number of youth went for archery  [tex]'n(B)'= 22[/tex]

Substitute the value in the formula to get the number of youth participated in both '[tex]n(A\cap B)[/tex]'  we get,

[tex]37 = 24 +22-n(A\cap B)\\\\\implies n(A\cap B) = 46-37\\\\\implies n(A\cap B) =9[/tex]

Hence, the number of youths participated in both canoeing and archery is equal to [tex]9.[/tex]

Learn more about numbers here

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