Respuesta :
Solution:
The word problem needs to be developed into mathematical expressions.
[tex]\begin{gathered} \text{Let l represent Latoya} \\ a\text{ represents Austin} \\ j\text{ represents Jim} \end{gathered}[/tex]Developing the statements given;
[tex]\begin{gathered} \text{Latoya, Austin and Jim sent a total of 92 messages. This means;} \\ l+a+j=92\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\text{.}\mathrm{}(1) \\ \\ \text{Latoya sent 7 more messages than Jim. This means;} \\ l=j+7\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots.(2) \\ \\ \\ Aust\text{in sent 3 times as many messages as Jim. This means;} \\ a=3j\ldots\ldots\ldots\ldots\ldots\ldots\ldots\text{.}\mathrm{}(3) \end{gathered}[/tex]Substituting equations (2) and (3) into equation (1);
[tex]\begin{gathered} l+a+j=92 \\ (j+7)+3j+j=92 \\ \text{Collecting the like terms,} \\ j+3j+j=92-7 \\ 5j=85 \\ \text{Dividing both sides by 5 to get j;} \\ j=\frac{85}{5} \\ j=17 \end{gathered}[/tex]Substituting the value of j in equation (2) and equation (3) to get l and a respectively ;
[tex]\begin{gathered} l=j+7 \\ l=17+7 \\ l=24 \\ \\ \\ a=3j \\ a=3(17) \\ a=3\times17 \\ a=51 \end{gathered}[/tex]Therefore,
Latoya sent 24 messages
Austin sent 51 messages
Jim sent 17 messages.
