We read your photo as:

A survey of 40 houses revealed that 26 receive The Graphic and 24 receive The Times. 10 houses receive both. How many houses receive only The Times?

Mathematics

ScanSolve AI Answer

Answer

14\text{14}

Step-by-step solution

2 steps

** (continued):**
Let GG be the set of houses receiving Graphic and TT be the set of houses receiving Times.
Total houses, n(G∪T)=40n(G \cup T) = 40.
Number of Graphic copies, n(G)=26n(G) = 26.
Number of Times copies, n(T)=24n(T) = 24.

  1. Use the Principle of Inclusion-Exclusion to find the number of houses receiving both newspapers.

    The formula is n(G∪T)=n(G)+n(T)−n(G∩T)n(G \cup T) = n(G) + n(T) - n(G \cap T).
    Substitute the given values:

    40=26+24−n(G∩T)40 = 26 + 24 - n(G \cap T) 40=50−n(G∩T)40 = 50 - n(G \cap T) n(G∩T)=50−40n(G \cap T) = 50 - 40 n(G∩T)=10n(G \cap T) = 10

    So, 10 houses receive both Graphic and Times.

  2. Find the number of houses which receive Times only.

    The number of houses receiving Times only is n(T)−n(G∩T)n(T) - n(G \cap T).

    n(Times only)=24−10n(\text{Times only}) = 24 - 10 n(Times only)=14n(\text{Times only}) = 14

    The number of houses which receive Times only is 14\text{14}.

Was this helpful?

Try one yourself

A new problem that tests the same skill.

Still stuck on this one?

Ask a follow-up, and the answer starts from this question.

Got a different question?Ask your own question
Handwritten step-by-step solution preview

Handwritten Step-by-Step Solution

Get this as a handwritten image on WhatsApp — like a tutor wrote it for you.

Try on WhatsApp