Yolanda, dale, and tony sent a total of 114 text messages over their cell phones during the weekend. tony sent 3 times as many messages as yolanda. yolanda sent 6 more messages than dale. how many messages did they each send?

Define:

Let the number of messages Dale sent= x

The number of messages Yolanda sent = x + 6

The number of messages Tony sent = 3(x + 6)

Equation:

x + (x + 6) + 3(x + 6) = 114

x = 19

Dale = 19

Yolanda = 25

Tony = 75

Dale = 18 messages

Yolanda = 24 messages

Tony = 72 messages

Step-by-step explanation:

Total messages send = 114 (1)

Let Dale send = x messages   (2)

Therefore Yolanda send =  ( 6 + x ) messages  (3)

Therefore, Tony send  = 3( 6 + x ) messages  (4)

Thus equating (1),(2),(3) and (4), we get

x + ( 6 + x ) + 3( 6 + x ) = 114

x +  6 + x  + 18 + 3x  = 114

5x +18 = 114

∴ x = 18

Dale send messages = x  = 18 messages

Yolanda send messages =  ( 6 + x )

                                          =   6 + 18 = 24 messages

Tony send messages = 3( 6 + x )

                                      = 3 x 24 = 72 messages