Question

Yolanda, Ryan, and Henry sent a total of 127 text messages during the weekend. Ryan sent 7 more messages than Yolanda. Henry sent 4 times as many messages as Yolanda. How many messages did they each send?

Answer 1

• Yolanda: 20
• Ryan: 27
• Henry: 80

Explanation:

You want the number of text messages sent by each of Yolanda, Ryan, and Henry if they sent a total of 127, and Ryan sent 7 more than Yolanda, while Henry sent 4 times as many as Yolanda.

Setup

The relationships expressed in the problem statement can be written as equations:

• y +r +h = 127
• r = y +7
• h = 4y

Solution

Using the last two equations to substitute into the first, we have ...

y +(y +7) +(4y) = 127

6y = 120 . . . . . . . . . . . . subtract 7

y = 20 . . . . . . . . . . . divide by 6

r = 20 +7 = 27

h = 4·20 = 80

Yolanda sent 20 text messages, Ryan sent 27, and Henry sent 80.