Question

laura deon and ravi sent a total of 101 text messages during the weekend. ravi sent 2 times as many messages as deon laura sent 9 more messages than deon how many messages did they each send

Answer 1

Step 1: Represent laura, deon and ravi

`\begin{gathered} \text{let l represents laura's sent messages} \\ \text{let d represents deon's sent messages} \\ \text{let r represents Ravi's sent messages} \end{gathered}`

Step 2: Write the relationship between l, d, and r from the first statement

`l+d+r=101`

Step 3: Write the relationship from the second statements

`\begin{gathered} r=2d \\ l=d+9 \end{gathered}`

Step 4: Substitute the r and l in the first relationship

`\begin{gathered} l+d+r=101 \\ d+9+d+2d=101 \\ d+d+2d=101-9_{} \\ 4d=92 \\ d=(92)/(4) \\ d=23 \end{gathered}`

Step 5: Solve for r and l

`\begin{gathered} r=2d \\ r=2*23=46 \end{gathered}`
`\begin{gathered} l=d+9 \\ l=23+9 \\ l=32 \end{gathered}`

Hence, Ravi sent 46 messages, Deon sent 23 messages, and Laura sent 32 messages