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Luis spent a certain amount of money in a supermarket. He spent a thir

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Luis spent a certain amount of money in a supermarket. He spent a thir  [#permalink]

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New post 26 Jul 2019, 08:00
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Luis spent a certain amount of money in a supermarket. He spent a third of the money on fruits, a sixth on vegetables, $12 on pasta, half the remainder of the money on chocolate, and as much on soda as he spent on vegetables. How much money did Luis spend in the supermarket?

A. 60
B. 66
C. 72
D. 78
E. 84

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Re: Luis spent a certain amount of money in a supermarket. He spent a thir  [#permalink]

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New post 26 Jul 2019, 08:11
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1
Luis spent a certain amount of money in a supermarket. He spent a third of the money on fruits, a sixth on vegetables, $12 on pasta, half the remainder of the money on chocolate, and as much on soda as he spent on vegetables. How much money did Luis spend in the supermarket?
A. 60
B. 66
C. 72
D. 78
E. 84

let total money be 72
so Fruits ; 24 ; Vegetable ; 12 ; Pasta ; 12 ; total 48
left with 24 half is 12 chocolate and soda ; 12
total 72
IMO C
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Luis spent a certain amount of money in a supermarket. He spent a thir  [#permalink]

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New post Updated on: 26 Jul 2019, 17:55
2
Let the total spent = x

--> Spent on fruits = x/3
--> Spent on vegetables = x/6
--> Spent on pasta = 12

Remainder amount = x - (x/3 + x/6 + 12) = x - x/2 - 12 = x/2 - 12

--> Spent on chocolate = 1/2*(x/2 - 12) = x/4 - 6
--> Spent on soda = x/6

Now, Total = x/3 + x/6 + 12 + (x/4 - 6) + x/6
--> x = 2x/3 + x/4 + 6
--> x = (8x + 3x + 72)/12
--> 12x = 11x + 72
--> x = 72 $

IMO Option C

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Originally posted by Dillesh4096 on 26 Jul 2019, 08:22.
Last edited by Dillesh4096 on 26 Jul 2019, 17:55, edited 1 time in total.
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Luis spent a certain amount of money in a supermarket. He spent a thir  [#permalink]

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New post Updated on: 27 Jul 2019, 20:20
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Now I get it.
It's 72.
after all deductions, we are left with 12.
and a 6th of 72 is 12.

Picking up an answer choice worked well.
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Originally posted by Prasannathawait on 26 Jul 2019, 08:25.
Last edited by Prasannathawait on 27 Jul 2019, 20:20, edited 1 time in total.
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Re: Luis spent a certain amount of money in a supermarket. He spent a thir  [#permalink]

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New post 26 Jul 2019, 08:27
2
Say the total money be x.

The Eqn:

\(\frac{x}{3}\) + \(\frac{x}{6}\) + \(12\) + \(\frac{1}{2}\) ( \(x\) - \(\frac{x}{3}\) - \(\frac{x}{6}\) - \(12\) ) + \(\frac{x}{6}\) = \(x\)

Now solving for \(x\) , we get the total money as \(72\) ..... Ans C.
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Re: Luis spent a certain amount of money in a supermarket. He spent a thir  [#permalink]

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New post 26 Jul 2019, 08:29
1
We can solve either by taking x or by options.I went for options as equation looked fuzzy and complex.

started with C. Total Spent Money=72
Fruits: 1/3 of 72=24
vegetables: 1/6 of 72=12
pasta=12
remaining=72-24-12-12=24
chocolates=24/2=12
soda =12 (as much on soda as he spent on vegetables).
This option exactly matches all the cases and therefore option C is the answer.
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Re: Luis spent a certain amount of money in a supermarket. He spent a thir  [#permalink]

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New post 26 Jul 2019, 08:30
1
C

Pretty straight forward. Assume x is the total amount spent in supermarket.

So, x/3 - fruits
x/6 - vegetables
$12 - pasta
remainder is x - all of the above = x/2 - 12
half of remainder on chocolate, so x/4 - 6 - chocolate
remaining half on soda - same as vegetables

So, x/4 - 6 = x/6, solve for x, we get x = $72
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Re: Luis spent a certain amount of money in a supermarket. He spent a thir  [#permalink]

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New post 26 Jul 2019, 08:32
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Luis spent a certain amount of money in a supermarket. He spent a third of the money on fruits, a sixth on vegetables, $12 on pasta, half the remainder of the money on chocolate, and as much on soda as he spent on vegetables. How much money did Luis spend in the supermarket?

A. 60
B. 66
C. 72
D. 78
E. 84

Given : Luis spent a certain amount of money in a supermarket. He spent a third of the money on fruits, a sixth on vegetables, $12 on pasta, half the remainder of the money on chocolate, and as much on soda as he spent on vegetables.

Asked: How much money did Luis spend in the supermarket?

Let the money he spend in the supermarket be x

Money spent on fruits = x/3
Money spent on vegetables = x/6
Money spent on fruits and vegetables = x/3+x/6 =x/2
Money spent on pasta = $12
Remaining money = x - (x/2 + 12) = x/2 -12
Money spent on chocolate = x/4 - 6
Money spent on soda = x/6

Total money spent = x/2 + 12 + x/4 -6 + x/6 = x
11x/12 +6 = x
x/12 = 6
x = 12*6 = 72

IMO C
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Luis spent a certain amount of money in a supermarket. He spent a thir  [#permalink]

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New post Updated on: 26 Jul 2019, 22:38
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Let, “X” be the total amount of money that Luis spent in a supermarket.

A third of the money on fruits: \(\frac{X}{3}\)
A sixth on vegetables: \(\frac{X}{6}\)
$12 on pasta: \(12\)
Half the remainder of the money on chocolate:
Let’s calculate the remainder first:\(X – [\frac{X}{3} + \frac{X}{6} + 12] = \frac{3X – 72}{6}\)
Hence, Half the remainder = \(\frac{3X – 72}{12}\) -> (a)

Rest on soda. As much on soda as he spent on vegetables: \(\frac{X}{6}\) -> (b)

If (a) and (b) both are half the remainders, then (a) = (b)
i.e. \(\frac{3X – 72}{12}\) = \(\frac{X}{6}\) => X = 72

Answer C

Originally posted by Sayon on 26 Jul 2019, 08:32.
Last edited by Sayon on 26 Jul 2019, 22:38, edited 1 time in total.
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Re: Luis spent a certain amount of money in a supermarket. He spent a thir  [#permalink]

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New post 26 Jul 2019, 08:35
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Luis spent a certain amount of money in a supermarket. He spent a third of the money on fruits, a sixth on vegetables, $12 on pasta, half the remainder of the money on chocolate, and as much on soda as he spent on vegetables. How much money did Luis spend in the supermarket

Given
\(1/3\) - fruits
\(1/6\)- vegetables
12$ - pasta

if chocolate is half the remainder then soda is another half
if soda =\(1/6\) then chocolate =\(1/6\) too

using this data, create an equation
\(1/3+1/6+x\)(this is pasta) \(+1/6+1/6=1\)
\(x=1/6\)
thus \(12$=1/6\)
Then the amount of money Luis spend in the supermarket \(= 12*6=72\)

The answer is C
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Luis spent a certain amount of money in a supermarket. He spent a thir  [#permalink]

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New post Updated on: 26 Jul 2019, 18:49
1
certain amount: x

List of expenses
Fruits:x/3
Vegetables: x/6
pasta:12
chocolate:x/2 - x/6 - x/12 - 6
soda:x/6

so, we have that:

x/3 + x/6 + 12 + x/2 - x/6 - x/12 - 6 + x/6 = x

6 = x/12
x=72

So (C) is our answer

Originally posted by Mizar18 on 26 Jul 2019, 08:40.
Last edited by Mizar18 on 26 Jul 2019, 18:49, edited 1 time in total.
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Re: Luis spent a certain amount of money in a supermarket. He spent a thir  [#permalink]

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New post 26 Jul 2019, 08:42
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IMO answer is C:

wring the equation as:
D/3+D/6+12+(D-(D/3+D/6+12))/2+D/6 = D

answer for this equation will be 72
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Re: Luis spent a certain amount of money in a supermarket. He spent a thir  [#permalink]

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New post 26 Jul 2019, 08:43
1
Quote:
Luis spent a certain amount of money in a supermarket. He spent a third of the money on fruits, a sixth on vegetables, $12 on pasta, half the remainder of the money on chocolate, and as much on soda as he spent on vegetables. How much money did Luis spend in the supermarket?

A. 60
B. 66
C. 72
D. 78
E. 84



Equation we have

1/3x+1/6x+12+1/2(x-(1/3x+1/6x+12))+1/6x=x

Resolving this we get x=72

Hence C
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Luis spent a certain amount of money in a supermarket. He spent a thir  [#permalink]

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New post Updated on: 26 Jul 2019, 09:18
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Quote:
Luis spent a certain amount of money in a supermarket. He spent a third of the money on fruits, a sixth on vegetables, $12 on pasta, half the remainder of the money on chocolate, and as much on soda as he spent on vegetables. How much money did Luis spend in the supermarket?

A. 60
B. 66
C. 72
D. 78
E. 84


total=fruits+vegetables+pasta+chocolate+soda
total=x
fruits+vegetables+pasta=x/3+x/6+12=3x/6+12=(3x+72)/6
chocolate=[x-((3x+72)/6)]/2=[6x-3x-72/6…(3x-72)/6]/2=(3x-72)/12
soda=x/6

x=(3x+72)/6+(3x-72)/12+x/6
x=(6x+144+3x-72)/12+x/6
x=(9x+72)/12+x/6
x=(9x+72+2x)/12
12x=11x+72
x=72

Answer (C).

Originally posted by exc4libur on 26 Jul 2019, 08:43.
Last edited by exc4libur on 26 Jul 2019, 09:18, edited 1 time in total.
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Re: Luis spent a certain amount of money in a supermarket. He spent a thir  [#permalink]

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New post 26 Jul 2019, 08:43
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Using PoE

A. 60
20-> fruits 10 -> Veggies 12 -> Pasta 9 -> C 10 -> Soda -- does not add up to 60
B. 66
33 -> 11 -> 12 -> 5 -> 11 -- adds upto more than 66
C. 72
24 -> 12 -> 12 -> 12 -> 12 -- adds upto 72 -- CORRECT
D. 78
E. 84

So, C
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Luis spent a certain amount of money in a supermarket. He spent a thir  [#permalink]

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New post Updated on: 26 Jul 2019, 12:16
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Let \(x\) be the total amount.

\(\frac{x}{3}= Fruits\)

\(\frac{x}{6}=Vegitables\)

\($12= Pasta\)

\(\frac{1}{2}(x-\frac{x}{3}-\frac{x}{6}-12)=Chocolate\) {This is half of the remaining amount}

\(\frac{x}{6}= Soda\)


\(\frac{x}{3} + \frac{x}{6} + 12 +\frac{1}{2}(x-\frac{x}{3}-\frac{x}{6}-12) + \frac{x}{6} = x\)

\(\frac{x}{3}+\frac{x}{3}+12 + \frac{1}{2} ( x- \frac{x}{2} -12) = x\)

\(\frac{2x}{3}+ 12 + \frac{1}{2}(\frac{x}{2} - 12) = x\)

\(12 + \frac{x}{4}- 6 = \frac{x}{3}\)

\(6= \frac{x}{3} - \frac{x}{4}\)

\(6= \frac{x}{12}\)

Thus, \(x= 12*6 =72\)

Answer is Total Amount= 72.

Originally posted by Ajiteshmathur on 26 Jul 2019, 08:49.
Last edited by Ajiteshmathur on 26 Jul 2019, 12:16, edited 1 time in total.
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Re: Luis spent a certain amount of money in a supermarket. He spent a thir  [#permalink]

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New post 26 Jul 2019, 08:50
Luis spent a certain amount of money in a supermarket. He spent a third of the money on fruits, a sixth on vegetables, $12 on pasta, half the remainder of the money on chocolate, and as much on soda as he spent on vegetables. How much money did Luis spend in the supermarket?

Take the total money he has is 90.
1/3 is 30
1/6 = 15
12 on pasta
remaining of chocolates and an equal amount in vegetables.


A. 60
B. 66
C. 72
D. 78
E. 84

IMO E.
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Re: Luis spent a certain amount of money in a supermarket. He spent a thir  [#permalink]

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New post 26 Jul 2019, 08:51
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Let total amount be x

on fruits = x/3
on vegetables = x/6
on pasta = $12
on chocolate = (x/2 - 12)/2
on soda = x/3
x/3 + x/6 + 12 + (x/2 - 12)/2 + x/3 = x
x = 72

C is correct.
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Re: Luis spent a certain amount of money in a supermarket. He spent a thir  [#permalink]

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New post 26 Jul 2019, 08:51
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total amount=x
Amount spent on Fruits=x/3
Amount spent on Vegetables=x/6
Soda=x/6
amount spent on chocolate is (x-(x/3+x/6+12))/2
so the equation boils down to 11x/12+6=x
x/12=6 and x=72
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Re: Luis spent a certain amount of money in a supermarket. He spent a thir  [#permalink]

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New post 26 Jul 2019, 08:55
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Luis spent a certain amount of money in a supermarket. He spent a third of the money on fruits, a sixth on vegetables, $12 on pasta, half the remainder of the money on chocolate, and as much on soda as he spent on vegetables. How much money did Luis spend in the supermarket?

Let's say the total amount = x
Fruits = x/3
Veggies = x/6
Pasta = 12

How much spent till now?
=x/3+x/6+12
=12+3x/6
=12+x/2

How much remained?
=x-(12+x/2)
=x/2-12

Half the remainder of the money on chocolate.
So, chocolate = (x/2-12) / 2
Soda = Veggies = x/6

Total shall be,
x = x/3+2x/6+(x-24) / 4 + 12
x-12 = 16x+6x - (24*6)
22x - (24*8) = 24x - (12*24)
2x = (12*24) - (8*24)
2x = 24 * (12-6)
2x = 24*6
x=72

So, answer should be (C)
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Re: Luis spent a certain amount of money in a supermarket. He spent a thir   [#permalink] 26 Jul 2019, 08:55

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