Question

Jessica, Miguel, and Dan sent a total of 75 text messages over their cell phones during the weekend. Dan sent 3 times as many messages as Jessica. Jessica sent 10 more messages than Miguel. How many messages did they each send?

Answer 1

Answer:

number of messages sent by Jessica = 17

Number of messages sent by Miguel = 7

Number of messages sent by Dan = 51

Step-by-step explanation:

Let number of messages sent by Jessica = $x$

As per given statement,

Number of messages sent by Dan = $3 \imes x$ and

Number of messages sent by Jessica are 10 more than that of Miguel.

So, Number of messages sent by Miguel are 10 lesser than that of Jessica.

Number of messages sent by Miguel = $x-10$

It is also given that,

Total number of messages sent = 75

Adding the number of messages sent by each one of them and putting them equal to 75:

$x+3x+x-10=75\\\Rightarrow 5x-10=75\\\Rightarrow 5x=85\\\Rightarrow x=17$

So, number of messages sent by Jessica, $x$ = 17

Number of messages sent by Miguel, $x-10$ = 7

Number of messages sent by Dan, $3x$ = 3$\times$17 = 51