How many messages did they each send?

Question

Linda, Justin, and Sam sent a total of 67 text messages over their cell phones during the weekend. Sam sent 2 times as many messages as Linda. Linda sent 9 more messages than Justin. How many messages did they each send?

Answer 1

Let x = number of messages Linda sent.

Justin sent x - 9 messages

Sam sent 2x messages

Combine like terms and make them equal 67

4x - 9 = 67

Add 9 to both sides in order to isolate the variable

4x -9 + 9 = 67 + 9

4x = 76

Divide both sides by the coefficient, 4

4x ÷ 4 = 76 ÷ 4

x = 19

Linda sent 19 messages

Substitute 19 for x to find how many messages Justin and Sam each sent.

Justin sent x - 9 which is 19 - 9; 10 messages

Sam sent 2x which is 2 × 19; 38 messages

Add to check:

19 + 19 - 9 + 38 = 67