SOLUTION: Bernard spent 1/3 of his money on a book and 1/6 of his money on a file. He gave the rest of his money equally to 5 friends, if each friend received $5, how much money had he at fi

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: Bernard spent 1/3 of his money on a book and 1/6 of his money on a file. He gave the rest of his money equally to 5 friends, if each friend received $5, how much money had he at fi      Log On


   

Question 1202862: Bernard spent 1/3 of his money on a book and 1/6 of his money on a file. He gave the rest of his money equally to 5 friends, if each friend received $5, how much money had he at first?
Found 4 solutions by greenestamps, ikleyn, josgarithmetic, math_tutor2020:
Answer by greenestamps(13209) About Me  (Show Source):
You can put this solution on YOUR website!


1%2F3%2B1%2F6=2%2F6%2B1%2F6=3%2F6=1%2F2

Since he spent 1/2 of his money, he gave 1/2 of it to his friends.

Each of his 5 friends got $5, so he gave away a total of $25.

Since the $25 he gave away was 1/2 of the money he had, the original amount of money he had was $50.

ANSWER (informally): $50

If you want a formal algebraic solution (overkill for this simple problem -- but useful for a beginning algebra student....)

Let x = his original amount of money

He spent 1/3 of his money and then 1/6 of his money. Find the fraction he spent altogether.

%281%2F3%29x%2B%281%2F6%29x=%281%2F2%29x

Find the fraction of his money he had left.

x-%281%2F2%29x=%281%2F2%29x

The money he had left he divided equally among 5 friends -- i.e. each friend got 1/5 of what he had left. Determine the fraction of his original money that each friend got.

%281%2F5%29%28%281%2F2%29x%29=%281%2F10%29x

Use the fact that each friend got $5 to find the amount he had originally.

%281%2F10%29x=5
x=10%2A5=50

ANSWER: $50

Answer by ikleyn(52884) About Me  (Show Source):
You can put this solution on YOUR website!
.
Bernard spent 1/3 of his money on a book and 1/6 of his money on a file. He gave the rest of his money
equally to 5 friends, if each friend received $5, how much money had he at first?
~~~~~~~~~~~~~~~~~~~


Strictly saying,  this problem is  SELF-CONTRADICTORY  and has no solution.

Indeed, the formal solution is  $50,  but (1/3)  of  $50  dollars has no integer value in cents;
as well as  (1/6)  of  $50  dollars has no integer value in cents.


The problem describes a situation,  which  NEVER  may  HAPPEN.


/////////////////


The problem's formulation is  INCORRECT,  since mathematically it is  IMPOSSDIBLE  to pay precisely  1/3  of  $50.

The tutors that support this incorrect mathematical formulation,  are all wrong with their solutions.



Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
----
Bernard spent 1/3 of his money on a book and 1/6 of his money on a file.
----

Starting at 1, all of his starting money
1-1%2F3-1%2F6
6%2F6-2%2F6-1%2F6
3%2F6
1%2F2-----he now had half of his starting money.

He gave this equally to 5 friends.
p at the start,
p%2F2 gave to five friends so each friend received p%2F10.

----
if each friend received $5, how much money had he at first?
----

p%2F10=5
p=10%2A5
highlight%28p=50%29

Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

1/3 + 1/6 = 2/6 + 1/6 = 3/6 = 1/2
In short,
1/3 + 1/6 = 1/2

Bernard spent 1/2 of his money on a book and a file.
The other 1/2 is given to his friends.

Each friend gets $5, so 5 friends total to 5*5 = 25 dollars given
x = total amount of money Bernard starts with
x/2 = amount given to friends
x/2 = 25
x = 2*25
x = 50


Answer: $50