Question

I NEED HELP IMMEDIATELY!!! 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?

Answer 1

Allen- 144 cards

Jane- 288 cards

Bob- 36 cards

Explanation:

Here's what we know:

a = 4b (Allen has 4 times Bob's cards)

j = 2a (Jane has twice Allen's)

a + j = 432 (Allen and Jane have 432 cards all together)

Start with substituting:

4b + 2a = 432

4b + 2(4b) = 432

Distribute:

4b + 8b = 432

Simplify:

12b = 432

Divide both sides by 12:

b = 36

To find how much Allen has just multiply 36 times 4.

a= 144 cards

To find how much Jane has multiply 144 times 2.

j= 288 cards

Answer 2

156

312 and

39

Explanation:

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