Question

Question #47bd9

Answer 1

Jane sent `31` messages, Boris sent `24` messages, and Shen sent `48` messages.

Explanation:

We first list the details.

Number of messages sent by Jane `=x`.

Number of messages sent by Boris `=x-7`.

Number of messages sent by Shen `=2(x-7)`.

Total number of messages sent `=103`.

Hence, we can write:

`x+ (x-7)+2(x-7)=103`

Open the brackets and simplify.

`x+x-7+2x-14=103`

`4x-21=103`

Add `21` to each side.

`4x-21+21=103+21`

`4x=124`

Divide both sides by `4`.

`(4x)/4=124/4`

`(1cancel4x)/(1cancel4)=31`

`x=31`

Jane sent `31` messages.

Boris sent `(x-7)=(31-7)=24` messages.

Shen sent `2(x-7)=2xx24=48` messages.

To check:

`31+24+48=103`