The membership in the math club at Rogers Junior High increased by 5% from last year to this year. The president of the math club used the following expression to find the number of members in the club this year.

Question

Which of the following is another expression that could be used to get the same result, and what does it represent?
A.
m + 1.05. This represents 1.05% of the members in the math club from last year.
B.
m + 5. This represents 5% of the members in the math club from last year.
C.
105m. This represents 105% of the members in the math club from last year.
D.
1.05m. This represents 105% of the members in the math club from last year.

Answer 1

To determine which alternative expression correctly represents the increase in membership in the math club, let's understand the context:

Let \( m \) be the number of members in the math club last year. An increase of 5% from last year to this year can be represented as:

1. The original number of members last year is \( m \).
2. The additional members due to the increase is \( 0.05m \) (which is 5% of \( m \)).
3. Therefore, the total number of members this year can be calculated as: \[ m + 0.05m = 1.05m \]

Now, let's analyze each of the provided options:

A. \( m + 1.05 \): This represents \( m \) (the number of members last year) plus 1.05. This is incorrect.

B. \( m + 5 \): This represents \( m \) (the number of members last year) plus 5. This assumes that 5 is the number of members added, not representing a percentage; hence it is incorrect.

C. \( 105m \): This suggests multiplying the number of members last year \( m \) by 105, which actually implies increasing the number by 105 times, so this representation is incorrect.

D. \( 1.05m \): This correctly represents an increase of 5% from last year, as it calculates 105% of \( m \) (which is the original plus the 5% increase).

Thus, the correct answer is:

D. \( 1.05m \). This represents 105% of the members in the math club from last year.