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 system of inequity is

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

the solid line passing through the points (0,4) and (4,0).

the related equation of solid line is .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

the related equation of dashed line is

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be . the required inequality is

similarly, check the second related equation.

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is