Question

Heather, Ahmad, and Pablo sent a total of 76 text messages during the weekend. Pablo sent 2 times as many messages as Ahmad. Heather sent 8 fewer messages than Ahmad. How many messages did they each send?

Answer 1

well, we know all three sent altogether 76 text messages
so... let us say, the amount of text for each is
Heather sent "h" amount
Ahmand sent "a" amount
and
Pablo sent "p" amount
so.. all three sent 76, meaning
h + a + p = 76
we know that, whatever "h" and "a" and "p" are

Pablo, send twice as much as Ahmad
so, if Ahmad sent "a", Pablo then sent 2 * a or 2a

Heather sent 8 less than Ahmad
so, if Ahmad sent "a", Heather then sent a - 8

thus
`\bf \begin{array}{llllll} h&+&a&+&p&=76\\ \uparrow &&&&\uparrow \\ a-8&&&&2a \end{array} \implies (a-8)+a+(2a)=76`

solve for "a", to find how many Ahmad sent
Heather sent 8 less than that
and
Pablo sent, twice as much

Answer 2

Ahmad - 21 (x)
Pablo - 42 (2x)
Heather - 13 (x-8)

2x + x + x - 8 = 76