SOLUTION: Sheik had some $2, $5 and $10 notes. The ratio of the number of $2 notes to the number of $5 notes to the number of $10 notes was 1:3:5. After spending all his $10 notes and 5/6 o

Question 1205615: Sheik had some $2, $5 and $10 notes. The ratio of the number of $2 notes to the number of $5 notes to the number of $10 notes was 1:3:5. After spending
all his $10 notes and 5/6 of his $5 notes, he had $783 left. How much money
did he have at first?
Found 3 solutions by math_tutor2020, josgarithmetic, greenestamps:
Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

Edit: I realize I made an error forming the equation. The error has been fixed.

x = number of $2 notes
3x = number of $5 notes
5x = number of $10 notes
Since x is a number of something, it can only be a positive whole number {1,2,3,4,...}

The ratio x:3x:5x reduces to 1:3:5 after dividing all parts by the GCF x.

He spends all of his $10 notes, so we ignore the 5x portion.
He spends 5/6 of his $5 notes and has 1/6 of those notes remaining.

2x = value of just the $2 notes
5*(1/6)*3x = 5*0.5x = 2.5 = value of the remaining $5 notes

2x+2.5x = 4.5x = total value of all of his remaining money

4.5x = 783
x = 783/(4.5)
x = 174

Then,
x = 174 = number of $2 notes
3x = 3*174 = 522 = number of $5 notes
5x = 5*174 = 870 = number of $10 notes

So,
2*174 + 5*522 + 10*870 = 11658
The total amount of money he started with is $11,658

Check:
He spent all 870 of the $10 notes, so he has 11658 - 10*870 = 2958 dollars remaining.
Then he spent 5/6 of the 522 copies of the $5 notes, meaning he spent 5*(5/6)*522 = 5*435 = 2175 further dollars.
He is ultimately left with 2958 - 2175 = 783 dollars which confirms the answer is correct.

Answer by josgarithmetic(39625)   (Show Source): You can put this solution on YOUR website!

NOTE VAL NOTE COUNT AFTER SPEND MONEY AFTER SPEND 2 x 2x *2x 5 3x (1/6)3x 5*(x/2) 10 5x 0 0 TOTAL 783

character-transposition mistake made.
------------------------------------------------------

~~This must almost certainly be a whole value but it is not.~~
~~Either the problem description or the question is wrong.~~
-------------------------------------------------------

This is better....
MONEY AFTER SPEND,

How much money had at first?

Answer by greenestamps(13203)   (Show Source): You can put this solution on YOUR website!

The other tutor has the right approach; but somewhere in his work there is an error, leading to a nonsensical solution....

x = # of $2 notes
3x = # of $5 notes
5x = # of $10 notes

He spent all of his $10 notes, so the number he had left was 0.

He spent 5/6 of his $5 notes, so the number he had left was (1/6) of 3x, or 0.5x.

He didn't spend any of his $2 notes, so the number he had left was x.

The value of his remaining notes was $783:

The amount he had at the start was

ANSWER: $11,658

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