Question

tom, ravi, and martina sent a total of 120 text messages over their cell - phones during the weekend. tom sent 4 times as many messages as ravi. ravi sent 6 fewer messages than martina. how many messages did they each send? write a text message ravi sent. write a text message tom sent. write a text message martina sent.

Explanation:

Step1: Let the number of messages Ravi sent be $x$.

Given Ravi sent $x$ messages.

Step2: Determine the number of messages Tom sent.

Tom sent 4 times as many messages as Ravi, so Tom sent $4x$ messages.

Step3: Let the number of messages Martina sent be $y$.

We know the total number of messages is 120, so $x + 4x+y=120$, which simplifies to $5x + y=120$. Given $x = 6$.

Step4: Substitute the value of $x$ to find the number of messages Tom sent.

Tom sent $4\times6 = 24$ messages.

Step5: Substitute $x = 6$ into the total - messages equation to find $y$ (messages Martina sent).

$5\times6+y=120$, so $30 + y=120$. Then $y=120 - 30=90$ messages.

Answer:

Ravi sent 6 messages, Tom sent 24 messages, Martina sent 90 messages.