Carmen, Reuben, and Jim sent a total of 156 text messages over their cell phones during the weekend. Jim sent 6 fewer messages than Carmen. Reuben sent 4 times as many messages as Jim. How many messages did they each send?

Step-by-step explanation:

1) determine what we know. We know that...

a) 156 total messages were sent

b) Jim sent 6 less that carmen

c) reuben sent 4 times as many as jim

2) create an equation with the information we know

(J= amount of messages jim sent, R= amount of messages reuben sent and C= amount of messages carmen sent)

(jim)         (reuben)     (carmen)    (total)

C - 6     +    J(4)    +    C            = 156

Now, isolate "C" on one side of the "="

3) add 6 to both sides of the equation:

C - 6 + J(4) + C =156

   -6                  -6

C + J(4) + C = 150

4) Combine like terms. In this case, combine the two Cs into Cx2:

C(2) +J(4) = 150

5) subtract "J(4)" from both sides of the "="

C(2) + J(4) = 150

        -J(4)     -J(4)

C(2) = 150 - J(4)

6) to isolate just 1 C, divide everything by 2

{C(2) = 150 - J(4)} ÷ 2

C = 75 - J(2)

7) Go back to our original equation (in bold) and replace "C" with "75 - J(2)"

(75-J(2)-6) + J(4) + (75-J(2)) = 156

Now solve for J.

Thats as far as I got.

the answer is true.

step-by-step explanation:

(a) the volume of the cone is 20/3 in3

hence, option a is correct.