Leila, Raphael, and Dionne Santa total of 101 text messages during the weekend. Dion sent 3 times as many messages as Leila. Rafael sent 6 more messages than Leila. How many messages did they send?

Question

Solution? Step by step ?

Answer 1

Hello Sophia,

So, the first thing we want to do is to assign some expressions for each person who used the phone and sent text messages, okay?

Therefore, let the following be true:

Leila = x <-------not given in the problem so we assign the value of x.

Dion = 3x <-------"Dion sent 3 times as many messages as Leila."

Rafael = x + 6 <-------"Rafael sent 6 more messages than Leila."

Please note: All quotes taken from the problem. I encourage you to underline the relevant parts of a problem when solving on your own so you can do this in the future.

Second, the problem tells us "Leila, Raphael, and Dionne Santa [sic] sent a "total of 101 text messages during the weekend." We are then asked "how many messages did they send?" In this last part of the question, I am supposing you mean how many did each send, right? To determine that information we sum the expressions together and set the equation equal to 101, okay? Therefore:

x + 3x + x + 6 = 101 <------All this is simply taking the three expressions and adding.

5x + 6 = 101 <------We combined like terms here.

5x = 95 <------We subtracted 6 from both sides of the equation.

x = 19

Third, we now substitute 19 for x in our original expressions, okay?

Leila = x = 19

Dionne = 3x = 3(19) = 57

Rafael = x + 6 = 25

Now, we check our work. The question is whether the three answers we obtained equal 101?

19 + 57 + 25 = 101?

101 = 101

Yes, the answer checks out and is valid. Another way you can check your work is to simply substitute the value of 19 into the original equation we had which was as follows:

x + 3x + x + 6 = 101

(19) + 3(19) + 19 + 6 = 101

19 + 57 + 19 + 6 = 101

101 = 101

Either way of checking your work is okay, but I wanted to provide you with the two ways you can do so.

I hope I have been of assistance to you and wish you a good Friday. If you need clarity to my solution, please just leave a comment below. If you wish to provide feedback, please leave a comment below. If you need further one on one assistance, please let me know through messaging me, or contacting any tutor! Best!