Weird advanced math word problem???

Question

A merchant pays duty on certain goods at three different places. At the first he gives 1/3 of goods, at the second 1/4(of the remainder), at the third 1/5(of the remainder). The total duty is 24. What was the original amount of goods???

I am confused?? Do I multiply all the fractions, if so why? Do I subtract?? Is the answer 40? Is the answer 1440? WHY AND HOW PLEASE???

Answer 1

yes.. the answer is 40 ....

let x = amount of goods....

1st payment = (1/3) x, and ( 2/3) x ..remains...

2nd payment = (1/4) of ( 2/3) x = ( 1/6) x , with 3/4 of your 2/3 of x remaining... so you have...(3/4)(2/3) x = ( 1/2 ) x left ....

3rd payment.... ( 1/5 ) of ( 1/2 ) x = ( 1/10) x


so ( 1/3) x + ( 1/6) x + ( 1/10 ) x = 24
multiply by 30........ 10x + 5x + 3x = 720

18x = 720 , x = 40

you may check your work by substitution ...
( 40 / 3 ) + ( 40 / 6 ) + ( 40 / 10 ) = 24


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don't forget to make a choice for Best Answer....

Answer 2

let x be the total amount of goods

he gives 1/3 of the goods. that means there are 2/3 of the goods left. Then he gives 1/4 of the remainder.
there are 2/3 - (1/4)(2/3) = 1/2 of the goods left. Then he give 1/5 of the remainder. there are 1/2 - (1/5)(1/2) = 2/5 of the goods left.

given that the total number of goods he gives a way is 24

(1/3)x + (1/4)(2/3)x + (1/5)(1/2) = 24
(1/3)x + (1/6)x + (1/10)x = 24
(3/5)x = 24
x = 40 <== answer

Answer 3

Let x = original amount of goods

1st duty:
= 1/3x

2nd duty:
= 1/4(x - 1/3x)
= 1/4(2/3x)
= 1/6x

3rd duty:
= 1/5(x - 1/3x - 1/6x)
= 1/5(6/6x - 2/6x - 1/6x)
= 1/5(1/2x)
= 1/10x

1/3x + 1/6x + 1/10x = 24
10/30x + 5/30x + 3/30x = 24
3/5x = 24
x = 40

Answer: 40 is the original amount of goods.

Proof:
1st duty
= 1/3 * 40 or 13 1/3

2nd duty
= 26 2/3 * 1/4
= 80/3 * 1/4
= 20/3 or 6 2/3

3rd duty
= 1/5(26 2/3 - 6 2/3)
= 1/5 of 20 or 4

Sum of duties is 24:
= 13 1/3 + 6 2/3 + 4
= 40/3 + 20/3 + 12/3
= 72/3 or 24

Answer 4

Let x be the original amount of goods
(1/3)x + (1/4)(x - (1/3)x) + (1/5)(x - (1/3)x - (1/4)(x - (1/3)x)) = 24
(1/3)x + (1/6)x + (1/10)x = 24
(3/5)x = 24
x = 40

Answer 5

Original amount of goods: x

Duty at first stage: x/3
Remaining amount: x - x/3 = 2x/3

Duty at second stage: 2x/3 * 1/4 = x/6
Remaining amount: 2x/3 - x/6 = x/2

Duty at third stage: x/2 * 1/5 = x/10
Remaining amount: x/2 - x/10 = 2x/5

Total duty = x - 2x/5 = 3x/5
3x/5 = 24
3x = 120
x = 40

The original amount of goods is 40

Answer 6

Let G be the original goods:
Stop 1: Pay G/3, continue with 2G/3
Stop 2: Pay (2G/3)/4, continue with (3/4)(2G/3)
Stop 3: Pay (3/4)(2G/3)/5, continue with (4/5)(3/4)(2G/3)
So, let G/3=H and 24=H+H/2+3H/10 =18H/10. Then H=15 and G=45

Answer 7

Let x represent the oringal amount.

24 = x + 1/3x + (1/4(1/3x)) + (1/5(1/4(1/3x)))

24 = 43/30x

24 / (43/30) = x

x = 720/43 (16.7441)

So... Yea.. I might of done it wrong though. Since x is his oringal amount, and he takes 1/3 of it at the first place. Then takes 1/4 of THAT (1/4(1/3 x)) and so on...

Answer 8

paying 1/3 leaves you with 2x/3.
paying 1/4 leaves you with 2x/3 *3/4.
paying 1/5 leaves you with 2x/3 * 3/4 * 4/5 = 2x/5
this is equal to 24.
2x/5 = 24
x = 60

Answer 9

the only way i could get close was to have just under 40, unless they r rounding

sorry itried all sorts of combos seems a factor is missing

Answer 10

;/.