SOLUTION: Hi Alan and Joe had the same amount of money. Alan spent 0.7 of his money while joe spent 0.2 . Joe bought 4 pens for $36 and found that he had twice as much money as Alan had lef

Question 1167413: Hi
Alan and Joe had the same amount of money. Alan spent 0.7 of his money while joe spent 0.2 . Joe bought 4 pens for $36 and found that he had twice as much money as Alan had left . How much money did they have altogether.
Thanks
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
i believe the problem statement should have been as follows:

Alan and Joe had the same amount of money.
Alan spent 0.7 of his money while joe spent 0.2 of his money.
Joe THEN bought 4 pens for $36 and found that he had twice as much money as Alan had left.
How much money did they have altogether?

when stated like this, you get the following.

Alan spent .7 * x, so he had .3 * x left.

Joe spent .2 * x, so he had .8 * x left.

joe then spent an additional 36 dollars.

this means he had .8 * x - 36 dollars left.

he then found that he had twice as much money left as Alan had.

this means that:

.8 * x - 36 = 2 * .3 * x

simplify to get:

.8 * x - 36 = .6 * x

subtract .6 * x from both sides of this equation and add 36 to both sides of this equation to get:

.2 * x = 36

solve for x to get:

x = 36 / .2 = 180.

this says they each had 180 dollars to start with.

alan spent 70% and so he had 30% left = .3 * 180 = 54 left.

joe spent 20% and so he had 80% left = .8 * 180 = 144 left.

joe then spent an additional 36 dollars and so he had 144 - 36 = 108 left.

he found that he had twice as money left as alan had left.

108 / 54 = 2, confirming what he found was correct.

since they each had 180 dollars to start with, then they both had 2 * 180 = 360 dollars to start with.

your solution is that the money that they had all together was 360 dollars before they had spent any money.

the original problem statement was confusing.

it was not clear that the 36 dollars that was spent was after .2 * x was spent.

i originally thought that the 36 dollars represented the .2 * x that was spent.

it turned out that, assuming that .2 * x = 36 provided me with logical inconsistencies that couldn't be resolved.

assuming the 36 was spent in addition to the .2 * x that was already spent removed the logical inconsistencies and so i went with that.

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