AMC 8 Daily Practice Round 11

Complete problem set with solutions and individual problem pages

Problem 23 Medium

In a school club, \frac{3}{4} of the members participate in community service, and \frac{9}{25} of the members are involved in academic competitions. A total of 44 members participate in both activities. How many members are involved only in academic competitions?

  • A.

    88

  • B.

    90

  • C.

    94

  • D.

    98

  • E.

    100

Answer:E

Let the total number of club members be represented as 1 unit. Using the inclusion-exclusion principle, the total number of members can be calculated as:

\text{Total members} = 44 \div \left( \frac{3}{4} + \frac{9}{25} - 1 \right).

Simplify the expression:

44 \div \left( \frac{111}{100} - 1 \right) = 44 \div \frac{11}{100} = 400 \ \text{members}.

The number of members involved only in academic competitions is:

400 \times \frac{9}{25} - 44 = 144 - 44 = 100.

Thus, the number of members involved only in academic competitions is \boxed{100}.

Related Problems
Problem 21 AMC 8 Daily Practice Round 11
Problem 22 AMC 8 Daily Practice Round 11
Problem 24 AMC 8 Daily Practice Round 11
Problem 25 AMC 8 Daily Practice Round 11
Think Academy Powered by ChatGPT