Question

Tammy, Michael, and Aldo sent a total of 119 text messages during the weekend. Tammy sent 9 more messages than Aldo. Michael sent 3 times as many messages as Aldo. How many messages did they each send?

Answer 1

Tammy = x

Michael = y

Aldo = z

x + y + z = 119 Eq 1

x = z +9 Eq 2

y = 3z Eq 3

We need to solve the equation system

Substitute eq 2 in 1

z + 9 + y + z = 119

y + 2z = 110 eq 4

Then we multiply eq 3 and 4

y + 2z = 110

-y + 3z = 0

5z = 110, z =22

then eq 3 will be rewritten as

y = 3x22 = 66

Finally we do the same with eq 2.

x = 22 + 9 = 31

So

Tammy sent 31

Michael 66

Aldo 22