FOUR QUESTION PROBLEM:
Amy and three friends launch a new website. Each of the four friends e-mails the web address to three new friends. These new friends forward the web address to three more friends. If no one receives the e-mails more than once, how many people will receive the web address in the second wave of e-mails?
1)Draw a pattern/diagram to model the situation for Amy.
2)How many e-mails are sent in each wave of Amy's diagram?
3)Amy is just one of four friends initiating the first wave of e-mails. Write an expression for the total number of e-mails sent in the 2nd wave.
4)Identify the computation that should be done first to simplify the expression in step-3. Then simplify the expression
THANK YOU!
1) Amy's diagram would look like this:
Amy --> 3 friends --> 3 friends --> 3 friends
2) In each wave of Amy's diagram, 3 e-mails are sent.
3) The total number of e-mails sent in the 2nd wave is 4 x 3 x 3 = 36.
4) The computation that should be done first to simplify the expression is to multiply 4 x 3 x 3. This simplifies to 36.
1) To model the situation for Amy, we can draw a diagram. Start with Amy in the center and draw three arrows representing the three friends she emails. Then, from each of those three friends, draw three more arrows representing the friends they email. Continue this pattern for two waves of emails.
2) In each wave of Amy's diagram, there are a total of 3 emails sent from each person. So in the first wave, Amy and her three friends each send 3 emails, resulting in a total of 4 * 3 = 12 emails. In the second wave, each of the 9 new friends from the first wave sends 3 emails, resulting in a total of 9 * 3 = 27 emails.
3) Since there are a total of 4 friends initiating the first wave, and each of them sends 9 emails in the second wave, the expression for the total number of emails sent in the second wave of emails is 4 * 9 = 36 emails.
4) The computation that should be done first to simplify the expression in step 3 is the multiplication of 4 and 9. So, 4 * 9 = 36. Therefore, the expression simplifies to 36 emails.
1) To draw a pattern/diagram to model the situation for Amy, you can start by representing Amy and her three friends as four individual nodes. Then draw three arrows from each friend to their three new friends, indicating that they are forwarding the web address. Finally, draw three arrows from each new friend to the next three friends, representing the second wave of emails.
2) In each wave, each person sends the web address to three new friends. Since there are four people in the initial wave, they would send a total of 4 * 3 = 12 emails in the first wave.
3) If Amy is just one of the four friends initiating the first wave of emails, we need to consider the total number of people in the second wave of emails. In the first wave, a total of 12 people received the web address because each person sent it to 3 new friends. So, for the second wave, each of those 12 people will send the web address to 3 more friends. Therefore, the total number of people in the second wave would be 12 * 3 = 36.
4) To simplify the expression for the total number of emails sent in the second wave, we need to calculate the total number of people who received the web address in the first wave. As mentioned earlier, there were 12 people in the first wave. So, the computation that should be done first is to multiply 12 (the number of people in the first wave) by 3 (the number of new friends each person sends the web address to).
Simplifying the expression, we find that the total number of people who will receive the web address in the second wave is 12 * 3 = 36.