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At a supermarket, John spent 1/2 of his money on fresh fruit

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At a supermarket, John spent 1/2 of his money on fresh fruit  [#permalink]

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New post 06 Aug 2012, 02:53
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At a supermarket, John spent 1/2 of his money on fresh fruits and vegetables, 1/3 on meat products, and 1/10 on bakery products. If he spent the remaining $6 on candy, how much did John spend at the supermarket?

(A) $60
(B) $80
(C) $90
(D) $120
(E) $180

Practice Questions
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Page: 154
Difficulty: 600

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Re: At a supermarket, John spent 1/2 of his money on fresh fruit  [#permalink]

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New post 06 Aug 2012, 02:53
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5
SOLUTION

At a supermarket, John spent 1/2 of his money on fresh fruits and vegetables, 1/3 on meat products, and 1/10 on bakery products. If he spent the remaining $6 on candy, how much did John spend at the supermarket?

(A) $60
(B) $80
(C) $90
(D) $120
(E) $180

John spent \(1-(\frac{1}{2}+\frac{1}{3}+\frac{1}{10})=\frac{1}{15}\) of his money on candy. Since we are told that he spent $6 on candy, then he spent total of \($6*15=90\) at the supermarket.

Answer: C.
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Re: At a supermarket, John spent 1/2 of his money on fresh fruit  [#permalink]

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New post 06 Aug 2012, 06:06
6
x/2+x/3+x/10 = 28x/30

2x/30=6, hence x =90
Ans C.
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Re: At a supermarket, John spent 1/2 of his money on fresh fruit  [#permalink]

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New post 10 Aug 2012, 04:14
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SOLUTION

At a supermarket, John spent 1/2 of his money on fresh fruits and vegetables, 1/3 on meat products, and 1/10 on bakery products. If he spent the remaining $6 on candy, how much did John spend at the supermarket?

(A) $60
(B) $80
(C) $90
(D) $120
(E) $180

John spent \(1-(\frac{1}{2}+\frac{1}{3}+\frac{1}{10})=\frac{1}{15}\) of his money on candy. Since we are told that he spent $6 on candy, then he spent total of \($6*15=90\) at the supermarket.

Answer: C.
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Re: At a supermarket, John spent 1/2 of his money on fresh fruit  [#permalink]

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New post 15 Jun 2013, 03:43
1
Simply pick number from answer...

80 will be out since not divisible by 3.

Lets try 90..according to question 1/2 of 90= 45, 1/3 of 90=30 and 1/10 of 90=9 then just add all of them i.e 45+30+9=84. Now 90-84=6 left for candy hence 90 will be the answer..

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Re: At a supermarket, John spent 1/2 of his money on fresh fruit  [#permalink]

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New post 15 Jun 2013, 04:11
2
Slightly different approach -

Let x be total amount, so

x/2+x/3+x/10+6=x, which turns out to be -
28x+180=30x
So x=90
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Re: At a supermarket, John spent 1/2 of his money on fresh fruit  [#permalink]

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New post 23 Dec 2013, 11:15
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Bunuel wrote:
SOLUTION

At a supermarket, John spent 1/2 of his money on fresh fruits and vegetables, 1/3 on meat products, and 1/10 on bakery products. If he spent the remaining $6 on candy, how much did John spend at the supermarket?

(A) $60
(B) $80
(C) $90
(D) $120
(E) $180

John spent \(1-(\frac{1}{2}+\frac{1}{3}+\frac{1}{10})=\frac{1}{15}\) of his money on candy. Since we are told that he spent $6 on candy, then he spent total of \($6*15=90\) at the supermarket.

Answer: C.


Hello, i don't understand the part of "$6*15=90" can you explain me please? Why 6 its multiplied by 15?
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Re: At a supermarket, John spent 1/2 of his money on fresh fruit  [#permalink]

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New post 26 Dec 2013, 02:11
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mandrake15 wrote:
Bunuel wrote:
SOLUTION

At a supermarket, John spent 1/2 of his money on fresh fruits and vegetables, 1/3 on meat products, and 1/10 on bakery products. If he spent the remaining $6 on candy, how much did John spend at the supermarket?

(A) $60
(B) $80
(C) $90
(D) $120
(E) $180

John spent \(1-(\frac{1}{2}+\frac{1}{3}+\frac{1}{10})=\frac{1}{15}\) of his money on candy. Since we are told that he spent $6 on candy, then he spent total of \($6*15=90\) at the supermarket.

Answer: C.


Hello, i don't understand the part of "$6*15=90" can you explain me please? Why 6 its multiplied by 15?


Hello, as Bunuel explained above, John spent 1/15 of his money (remaining of his money) on candy
==> The remaining = 1/15 of his money = $6
==> total money spent = 15/15 of the remaining = 15*6 = 90

Hope it's clear.
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Re: At a supermarket, John spent 1/2 of his money on fresh fruit  [#permalink]

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New post 09 Sep 2014, 23:06
Bunuel wrote:
At a supermarket, John spent 1/2 of his money on fresh fruits and vegetables, 1/3 on meat products, and 1/10 on bakery products. If he spent the remaining $6 on candy, how much did John spend at the supermarket?

(A) $60
(B) $80
(C) $90
(D) $120
(E) $180

Practice Questions
Question: 15
Page: 154
Difficulty: 600



solution...

let x be the money spent..

x/2 +x/3 +x/10 = x-6
taking LCM then

(15x+10x+3x )/30 = x-6

28x=30x-180
x=90
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Re: At a supermarket, John spent 1/2 of his money on fresh fruit  [#permalink]

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New post 20 May 2016, 04:27
2
1
Bunuel wrote:
At a supermarket, John spent 1/2 of his money on fresh fruits and vegetables, 1/3 on meat products, and 1/10 on bakery products. If he spent the remaining $6 on candy, how much did John spend at the supermarket?

(A) $60
(B) $80
(C) $90
(D) $120
(E) $180


Solution:

Let's let T = total number of dollars spent at the supermarket. With this variable we can set up an equation and determine T.

We are given that John spent 1/2 of his money on fresh fruits and vegetables, or (1/2)T, 1/3 on meat products, or (1/3)T, and 1/10 on bakery products, or (1/10)T. We are also given that he spent the remaining $6 on candy. Since we know where all his money was allocated, we can sum these values together and set the sum to T. So we have:

(1/2)T + (1/3)T + (1/10)T + 6 = T

To get rid of the fractions we can multiply the entire equation by 30, and we obtain:

15T + 10T + 3T + 180 = 30T

28T + 180 = 30T

180 = 2T

T = 90

John spent $90 at the supermarket.

Answer: C
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Re: At a supermarket, John spent 1/2 of his money on fresh fruit  [#permalink]

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New post 20 May 2016, 08:56
Total money spent= 1/2x+1/3x+1/10x= 28/30x

Money left = 2/30 or $6

2/30x=6
x= 90
C is the answer
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Re: At a supermarket, John spent 1/2 of his money on fresh fruit  [#permalink]

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New post 20 May 2016, 11:08
Bunuel wrote:
At a supermarket, John spent 1/2 of his money on fresh fruits and vegetables, 1/3 on meat products, and 1/10 on bakery products. If he spent the remaining $6 on candy, how much did John spend at the supermarket?

(A) $60
(B) $80
(C) $90
(D) $120
(E) $180

Practice Questions
Question: 15
Page: 154
Difficulty: 600


Let total amount be 60x

Money spent on fresh fruits and vegetables = 30x
Money spent on meat products = 20x
Money spent on bakery products = 6x

Total money spent 56x

Money left (4x) = 6

So, x = 1.5

So, total money John had initially is 1.5 x 60 => $90

Hence answer will be $90
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Re: At a supermarket, John spent 1/2 of his money on fresh fruit  [#permalink]

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New post 20 May 2017, 20:07
"How can one say, that candy is bought at supermarket only"

Answer 90 is correct when we assume the above statement else answer is 84.

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Re: At a supermarket, John spent 1/2 of his money on fresh fruit  [#permalink]

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New post 17 Dec 2017, 16:18
can someone give a link to forum on theory of ratios? Experts , mods?
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Re: At a supermarket, John spent 1/2 of his money on fresh fruit  [#permalink]

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New post 17 Dec 2017, 20:37
mtk10 wrote:
can someone give a link to forum on theory of ratios? Experts , mods?


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Re: At a supermarket, John spent 1/2 of his money on fresh fruit  [#permalink]

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New post 07 Jan 2018, 18:16
Bunuel niks18

Quote:
At a supermarket, John spent 1/2 of his money on fresh fruits and vegetables, 1/3 on meat products, and 1/10 on bakery products.


I began on wrong note while solving this on my own. Say X- amount he initially had.
I did not interpret Q as At a supermarket, John spent 1/2 of his money on fresh fruits and vegetables, 1/3 of his TOTAL money on meat products, and 1/10 (of his TOTAL money) on bakery products
and instead did spend/ receive at each stage:
at fruits and veg: spent - X/2 , Remaining - X/2 <- 1 - X/2
at meat - remaining - (X/2), spent X/6
messing the solution.

Can you add your two cents.
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Re: At a supermarket, John spent 1/2 of his money on fresh fruit  [#permalink]

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New post 07 Jan 2018, 19:46
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adkikani wrote:
Bunuel niks18

Quote:
At a supermarket, John spent 1/2 of his money on fresh fruits and vegetables, 1/3 on meat products, and 1/10 on bakery products.


I began on wrong note while solving this on my own. Say X- amount he initially had.
I did not interpret Q as At a supermarket, John spent 1/2 of his money on fresh fruits and vegetables, 1/3 of his TOTAL money on meat products, and 1/10 (of his TOTAL money) on bakery products
and instead did spend/ receive at each stage:
at fruits and veg: spent - X/2 , Remaining - X/2 <- 1 - X/2
at meat - remaining - (X/2), spent X/6
messing the solution.

Can you add your two cents.


Hi,
Nothing much to add to your query because you read the question wrong. NO where it is mentioned that REMAINING AMOUNT is spent in other items. Hence you will have to work with total amount.

As far as solution is concerned, when you see fractions it is always better to work with smart nos. which is LCM of the fractions.

So let he had 30 to spend (LCM of 2, 3, 10)

So he spent 15+10+3=28

Remaining 2 is equivalent to 6

Hence 30 will be equivalent to 6*30/2=90

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Re: At a supermarket, John spent 1/2 of his money on fresh fruit  [#permalink]

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New post 04 Feb 2018, 12:19
Hi All,

This question can be solved by TESTing THE ANSWERS.

We know that John has an unknown amount of money, but he spends it in the following way:
1/2 of the money is spent on fruit and vegetables
1/3 of the money is spent on meat
1/10 of the money is spent on bakery products.
AND then the remaining $6 is spent on candy.

Notice that the answer choices are all integers. Given that the fractions have a common-denominator of 30, the correct answer is likely a multiple of 30. By TESTing one of the two 'middle' multiples of 30 in the answers, we have a good chance of either finding the correct answer or being able to determine if we're 'too big' or 'too small' on the first try and get the correct answer without having to TEST more than one answer.

Let's TEST Answer C: $90

IF the total was $90, then...
$45 is spent on fruit and vegetables
$30 is spent on meat
$9 is spent on bakery products.

45+30+9 = 84
This leaves 90-84 = $6 which is exactly what the rest of the question states, so this MUST be the answer.

Final Answer:

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Re: At a supermarket, John spent 1/2 of his money on fresh fruit &nbs [#permalink] 04 Feb 2018, 12:19
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