Martina, Hong, and Felipe sent a total of 91 text messages

Question

Martina, Hong, and Felipe sent a total of 91 text messages over their cell phones during the weekend. Hong sent 9 more messages than Martina. Felipe sent 2 times as many messages as Hong. How many messages did they each send?

Answer 1

Answer: Martina sent 16 messages, Hong sent 25 messages, and Felipe sent 50 messages. The explanation follows.

 

Let's set up some algebraic expressions by translating the words into numbers and variables.

 

1. Hong sent 9 more messages than Martina. Let's say Martina sent x messages; therefore, Hong sent x+9 messages 

 

2. Felipe sent 2 times as many messages as Hong. Well, we just determined that Hong sent x+9 messages. That means that Felipe sent twice this number which equals 2(x+9)

 

3. Here is what we have so far:

    x=number of messages Martina sent

    x+9=number of messages that Hong sent

    2(x+9)=number of messages that Felipe sent

 

4. now we sum up all of our expressions to get the total number of messages sent which is 91 according to the problem

x+(x+9)+2(x+9)=91

 

5. Solve the above equation for x:

x+(x+9)+2(x+9)=91

2x+9+2(x+9)=91

2x+9+2x+18=91; in this step I simply distributed the 2 over (x+9)

4x+27=91

4x=64; in this step I subtracted 27 from both sides

x=16

 

5. x was defined as the number of messages that Martina sent therefore Martina sent 16 messages. x+9 was the number of messages that Hong sent therefore Hong sent 16+9=25 messages. Finally, 2(x+9) was the number of messages that Felipe sent; therefore Felipe sent 2(16+9)=2(25)=50 messages.

 

If this explanation was helpful, please vote it up. If not, please let me know how I may further assist you. 

 

Answer 2

let x = number of messages sent by Hong

     y = number of messages sent by Martina

     z = number of messages sent by Felipe

 

Then, x + y + z = 91

                      x = y + 9

                      z = 2x

 

Replace z by 2x in the first equation to get:

 

3x + y = 91

 x   - y = 9

 

Adding these two equations, we have 4x = 100.  So, x = 25.

 

Since x - y = 9 and x = 25, we obtain 25 - y = 9. So, y = 16.

Since z = 2x and x = 25, z = 50.

 

ANSWER:  Hong sent 25 messages, Martina sent

                16 messages, and Felipe sent 50 messages.