Question

Heather, Brian, and Rafael sent a total of 82 text messages over their cell phones during the weekend. Rafael sent times as many messages as Heather. Heather sent fewer messages than Brian. How many messages did they each send?

Answer 1

We define the following variables:

x = Heather

y= Brian

z = Rafael

x<y Heather sent fewer messages than Brian

x=z , Rafael sent times as many messages as Heather

Explanation:

The equation that solves this problem is

`x+y+z=82\\2x+y=82\\2x=82-y\\\\x=1/2(82-y)`

Remember that

`x<y\\1<=x<=27`

; we can define the following interval

for example 1)

`x=1/2(82-y)\\x=1\\2(1)=82-y\\2=82-y\\y=80\\x=z=1`

for example 2)

`2x=82-y\\ x=272(27)=82-y\\54=82-y\\y=28\\x=z=27\\`