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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?

 Apr 19, 2020
 #1
avatar+44 
+2

Writing everything in terms of Bob, Allen is 4 Bob, or b, and Jane is 2 Allen, or 2 * 4 = 8 Bob. In total, Jane and Allen are 12 Bob. 468/13 = 36, so 36 is Bobs amount, 36 * 4 = 144 is Allen, and 36 * 8  = 288.

Finally,

Bob: 36

Allen: 144

Jane: 288


Hope this helps!

 

Edit: Thanks lokiisnotdead for correction /13 instead of 12

 Apr 19, 2020
edited by shad0w  Apr 19, 2020
 #3
avatar+367 
+2

hmmm shadlow I think its 468/13 because x+4x+8x=13x.

lokiisnotdead  Apr 19, 2020
 #4
avatar+44 
+2

your right, i fixed my answer good catch!

shad0w  Apr 19, 2020
 #2
avatar+367 
+2

Hi guest!

 

Let's give variables to each of these people.

 

Bob = x

Allen = 4x

Jane = 2(4x) = 8x

 

Since they have 468 cards together, we know that

 \(x+4x+8x=468\)

\(13x=468\)

\(x=36\)

 

So, we know that Bob has 36 cards. Allen has 4(36)=144 cards. Jane has 8(36)=288 cards!

We can check this, 36+144+288=468!

 

I hope this helped you, guest!

:)

 Apr 19, 2020

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