Allen has four times as many cards as Bob, and Jane has twice as many cards as Allen. Together, Allen and Jane have 468 cards. How many cards do Allen, Jane, and Bob each have?

Let Allen be A , Jane be J and Bob be B

Allen has 4 times as Bob

So

A = 4B

Jane has twice as Allen

So

J = 2A

Together, Allen and Jane has 468 cards

A + J = 468

Substitute 2A for J in the third equation.

We have

A + J = 468

A + 2A = 468

3A = 468

Divide both sides by 3

3A/3 = 468/3

A = 156

Recall

A = 4B

Therefore

156 = 4B

Divide both sides by 4

156/4 = 4B/4

39 = B

B = 39

Also,

J = 2A

J =2 x 156

J = 312

Allen has 156 cards

Jane has 312 cards and

Bob has 39 cards

Step-by-step explanation:

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3

let's fu(!

step-by-step explanation: