Found 4 solutions by Edwin McCravy, ikleyn, timofer, mccravyedwin:
Answer by Edwin McCravy(20060) (Show Source): You can put this solution on YOUR website!
Bob and John had some cards.
Bob has B cards. John has J cards
When John gave Bob 32 cards then they would have an equal amount of cards.
J-32 = B + 32
If Bob gave John 161 cards then John would have 4 times as many cards as Bob.
4(B-161) = J+161
How many cards did Bob have.
Adding the equations term by term,
That's what I got, also.
Maybe they cut some cards up.
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Or maybe there was another way to interpret this. Let's reword it this way:
Bob and John had some cards.
John gave Bob 32 cards and then they had an equal amount of cards.
Beginning with an equal number of cards, Bob gave John 161 cards.
Then John had 4 times as many cards as Bob.
How many cards did Bob have?
Let's do it that way:
After John gave Bob 32 cards, they had N cards each.
Bob gave John 161 cards. Then Bob had N-161 cards and John had N+161 cards.
Then John had 4 times as many cards as Bob.
So originally John had 32 cards more and Bob had 32 cards less.
So in the beginning, John had and
Bob had
That also requires cutting cards in thirds.
I dunno. Obviously, your son's teacher was not savvy as to how to
make up word problems.
Edwin
Answer by ikleyn(52812) (Show Source): You can put this solution on YOUR website!
.
Bob and John had some cards.
When John gave Bob 32 cards then they would have an equal amount of cards.
If Bob gave John 161 cards then John would have 4 times as many cards as Bob. How many cards did Bob have.
My son found that Bob had 289 and two thirds cards. Can someone check this please.
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x = the number of cards Bob had initially.
Then the number of cards John had initially is (x+2*32) = (x+64).
"If Bob gave John 161 cards then John would have 4 times as many cards as Bob. "
In Math form, it means
Bob had John had
after after
giving getting
4 * (x - 161) = (x+64)+161.
Simplify and find x
4x - 644 = x + 225,
4x - x = 225 + 644,
3x = 869
x = 869/3 = 289.
The answer that your son got is correct, but makes no sense,
since the number of cards must be a non-negative integer number.
It means that the problem, as posted, printed and presented, is HEAVILY DEFECTIVE.
/\/\/\/\/\/\/\/\/\/\/\
Comment from student : Hi ikleyn Thank you for confirming the absurd answer. This is straight from the textbook.
My response : Report to the Publishing company or/and to the author, referring to
the precise textbook name, edition, year of edition, ISBN number,
then the section name, page number and the number of the problem.
Answer by timofer(105) (Show Source): You can put this solution on YOUR website!
"When John gave Bob 32 cards then they would have an equal amount of cards.
If Bob gave John 161 cards then John would have 4 times as many cards as Bob.
How many cards did Bob have."
The description or the question is wrong.
Answer by mccravyedwin(408) (Show Source): You can put this solution on YOUR website!
I think the error was that 161 should have been 163. The answer
comes out a whole number when you change 161 to 163.
So I think the problem should have been:
Bob and John had some cards. When John gave Bob 32 cards then they would have an equal amount of cards.
If Bob gave John 163 cards then John would have 4 times as many cards as Bob.
How many cards did Bob have?
Bob and John had some cards.
Bob has B cards. John has J cards
When John gave Bob 32 cards then they would have an equal amount of cards.
J-32 = B + 32
If Bob gave John 163 cards then John would have 4 times as many cards as Bob.
4(B-163) = J+163
How many cards did Bob have?
Adding the equations term by term,
So Bob had 293. <--ANSWER
Let's find out how many cards John had so we can check.
Bob had 293 and John had 357.
When John gave Bob 32 cards they an equal amount of cards.
John then had 357-32=325
Bob then had 293+32=325
Bob gave John 163 cards
John then had 357+163=520
Bob then had 293-163=130
Checking (130)(4) = 520
That shows John then had 4 times as many cards as Bob.
Edwin
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