Question

question 7 of 7
lavonne purchased some tickets and snack vouchers for an upcoming event and gave them to the members of her work group. each member of her work group received the same number of tickets and the same number of snack vouchers. the total number of tickets she gave to her group was 30, and the total number of snack vouchers was 75. which of the following could be the number of members in lavonnes work group?
10
15
25
30

Explanation:

Step1: Find GCD of 30 and 75

To find the number of members, we need a common divisor of 30 and 75. First, factorize 30 and 75.
$30 = 2\times3\times5$
$75 = 3\times5\times5$
The greatest common divisor (GCD) is $3\times5 = 15$.

Step2: Check divisors

The number of members must divide both 30 (total tickets) and 75 (total snack vouchers). Let's check the options:

• 10: $30\div10 = 3$, $75\div10 = 7.5$ (not integer, so invalid).
• 15: $30\div15 = 2$, $75\div15 = 5$ (both integers, valid).
• 25: $30\div25 = 1.2$ (not integer, invalid).
• 30: $75\div30 = 2.5$ (not integer, invalid).

Answer:

15 (the option with "15" as the number of members)