Question

Diane has a business selling candles to people at home sales parties. Wanting to get more people to hold parties for her, she offered to pay $30 to anyone who would hold a sales party as well as arranging for two more people to hold parties during the next month (each host holds just one party). It was a complete success! Every host was able to find two more people willing to host a party the following month. She started with three hosts in January. If this continues, how many parties will her business have held during the first 6 months?

Answer 1

Diane's business will have held a total of 24 parties during the first 6 months.

Step-by-step explanation:

Starting with three hosts in January, Diane's business will have held a total of 24 parties during the first 6 months.

Here's how we can calculate it:

1. In January, there are 3 hosts which equals 3 parties.
2. In February, each of the 3 hosts from January will hold a party and find 2 more hosts. This results in 6 new hosts, making a total of 9 hosts in February and 9 parties.
3. In March, each of the 9 hosts from February will hold a party and find 2 more hosts. This results in 18 new hosts, making a total of 27 hosts in March and 27 parties.
4. This pattern continues for April, May, and June, with each new month doubling the number of hosts and parties compared to the previous month.

Therefore, the number of parties held during the first 6 months will be:

January (3 parties) + February (9 parties) + March (27 parties) + April (81 parties) + May (243 parties) + June (729 parties) = 1092 parties.