# Math Help - Where is logic flaw?

1. ## Where is logic flaw?

Hi guys

Here is the question:

Jenny has 228 more marbles than jack. if bob gave each of them 133 marbles, she will have twice as many marbles as jack. How many marbles does jenny have?

I said (jn = jenny, jk = jack):

jn = jk+228
jn +133 = 2*jk

substitute jn-228 for jk in the 2nd equation:
jn +133= 2*(jn-228)

solve for jn:
jn=323

BUT why does this not work - it seems like it should???

jn = jk+228

Add 133 to jenny and jack:
jn +133= (jk+133)+228 = 2jk

jn+133 = jk+361 = 2jk

=> jk+361 =2jk
=> jk=361

so jn +133 = 361+228
and jn = 456

2. Originally Posted by B_Miner
Hi guys

Here is the question:

Jenny has 228 more marbles than jack. if bob gave each of them 133 marbles, she will have twice as many marbles as jack. How many marbles does jenny have?

I said (jn = jenny, jk = jack):

jn = jk+228
jn +133 = 2*jk

substitute jn-228 for jk in the 2nd equation:
jn +133= 2*(jn-228)

solve for jn:
jn=323

BUT why does this not work - it seems like it should???

jn = jk+228

Add 133 to jenny and jack:
jn +133= (jk+133)+228 = 2jk

jn+133 = jk+361 = 2jk

=> jk+361 =2jk
=> jk=361

so jn +133 = 361+228
and jn = 456

Let $J_n$ and $J_k$ represent Jenny and Jack respectively.

Jenny has 228 marbles more than Jack ==> $J_n=228+J_k$.

Bob gives them each 133 more -> Jenny now has twice as many marbles as Jack ==> $J_n+133=361+J_k=2J_k$

Thus, it follows that $361+J_k=2J_k\implies J_k=361$

Therefore, $J_n+133=2\left(361\right)\implies J_n=722-133=589$

Thus, Jenny has 589 marbles and Jack has 361 marbles.

Does this make sense?

3. Hi Chris-

The answer is 323 though (the first way I did it).

The second way I did it (and you did it) we both got jack = 361.
But depending on the substitution we made, we got different answers (both wrong).

Now I am really confused

4. Originally Posted by Chris L T521
Thus, Jenny has 589 marbles and Jack has 361 marbles.

Does this make sense?
But that cannot be correct, because Jenny is now supposed to have twice as many marbles as Jack, but 361 * 2 = 722, which does not equal 589.

5. Originally Posted by B_Miner
Hi Chris-

The answer is 323 though (the first way I did it).

The second way I did it (and you did it) we both got jack = 361.
But depending on the substitution we made, we got different answers (both wrong).

Now I am really confused
When I solved this, I got these values:

Jack had 95, Jenny had 323 (before bob gave them marbles). After bob gave them each 133, Jack has 228 and Jenny has 456.

Let x = # of marbles JACK has to start. Then, x + 228 equals the number of marbles JENNY has to start.

Each of these quantities increases by the same amount, 133, and after this, JENNY has twice as many marbles as JACK. So,

JACK's marbles JENNY's marbles
2 * (x + 133) = (x + 228 + 133)

Jenny's marbles are twice that of Jack's.

2x + 266 = x + 361
-x -266 = -x - 266

x = 95

This was the number of marbles JACK had to START, remember? So Jenny had 95 + 228 = 323. But remember, BOB gave them each 133 more marbles.

So
Jack has 95 + 133 = 228
Jenny has 323 + 133 = 456

6. Originally Posted by B_Miner
[snip]

Hi guys

Here is the question:

Jenny has 228 more marbles than jack. if bob gave each of them 133 marbles, she will have twice as many marbles as jack. How many marbles does jenny have?

I said (jn = jenny, jk = jack):

jn = jk+228
jn +133 = 2*jk

substitute jn-228 for jk in the 2nd equation:
jn +133= 2*(jn-228)

solve for jn:
jn=323

[/snip]

If you solve for $J_n$ in that equation, you get $J_n=589$, since

$J_n+133=2\left(J_n-228\right)\implies J_n+133=2J_n-456\implies 133+456=589=J_n$...

Originally Posted by B_Miner
Hi Chris-

The answer is 323 though (the first way I did it).

The second way I did it (and you did it) we both got jack = 361.
But depending on the substitution we made, we got different answers (both wrong).
Hm...

Now I am really confused
I'm starting to get there...

7. x = jenny original amount ........ (x - 228) = jack's original amount

x+133 = new amount for jenny ........ (x-228)+133 = x - 95 = jack's new amount

jenny now has twice what jack has ...

x+133 = 2(x - 95)

x+133 = 2x - 190

x = 323 , jenny's original amount ....... jack's original amount = 323-228 = 95

323+133 = 456 ........ 95+133 = 228

456 = 2(228)

8. Originally Posted by skeeter
x = jenny original amount ........ (x - 228) = jack's original amount

x+133 = new amount for jenny ........ (x-228)+133 = x - 95 = jack's new amount

jenny now has twice what jack has ...

x+133 = 2(x - 95)

x+133 = 2x - 190

x = 323 , jenny's original amount ....... jack's original amount = 323-228 = 95

323+133 = 456 ........ 95+133 = 228

456 = 2(228)
Hey, that's what I said.

9. Thanks everyone!!

I was starting to loose my marbles!

10. This is what you originally had:

Originally Posted by B_Miner

I said (jn = jenny, jk = jack):

jn = jk+228
jn +133 = 2*jk
... but what you should have started with was:

jn = jk+228
jn +133 = 2*(jk + 133)

... because after bob gave them BOTH 133 marbles, etc.