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Re: A dealer sold a total of 60 of the three appliances listed in the tabl [#permalink]
given
x+y+z=60
z=2x
30x+50y+120z= 4200
target find y/z
solve for y & z
2y+3z=120
10y+27z= 840
we get
z=20 & y = 30
y/z= 3/2
OPTION A


Bunuel

A dealer sold a total of 60 of the three appliances listed in the table above for a total of $4,200. If the dealer sold twice as many food processors as mixers, what was the ratio of the number of blenders sold to the number of food processors sold?

A. 3/2
B. 4/3
C. 6/7
D. 5/12
E. 1/3

PS20379


Attachment:
1.png
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Re: A dealer sold a total of 60 of the three appliances listed in the tabl [#permalink]
Let the mixer/piece be X
Blender be y
And food processor be Z.

30x+50y+120z=4200
3X+5y+12z=420
Since Z = 2x
3x+5y+12(2x)=420
27x+5y=420 --------(1)

Also x+y+z=60
X+y+2x=60
3x+y=60 --------(2)

Equating both,
=>27x+5y=420
=>(3x+y=60)*9

27x+9y=540
27x+5y=420
(Subtracting)
4y=120
Y=30 -----(3)

Putting value of y in equation 2
3x+y=60
3x=60-30
3x=30
X=10
Z=2x => z=20

(X,Y,Z) = (10,30,20)

Therefore the fraction of blender to food processor is 30/20=3/2
Answer is A

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Re: A dealer sold a total of 60 of the three appliances listed in the tabl [#permalink]
A.

Let Mixers sold = m
Blenders sold = b
Food Processors sold = f

Given m + b +f =60 --1
Also f:m = 2:1. or f =2m --2

Substituting 2 in 1
3m + b = 60
b = 60 - 3m --3

Total Price for m mixers = 30m

Total Price for b blenders = 50b

Total Price for f food processors =120f

Total price= 4200

Hence, 30m + 50b + 120 f = 4200

Substituting f= 2m and dividing by 10
27m + 5b = 420

Substituting b from eq 3
27m + 300 - 15m = 420
or m =10
f= 20
from 1, b = 30

b: f = 30:20 or 3:2
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A dealer sold a total of 60 of the three appliances listed in the tabl [#permalink]
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Answer: Option A

\(Mixer(M) + Blender(B) + Food processor(F) = 60\) and F = 2M (If the dealer sold twice as many food processors as mixers)

=> \(M + B + 2M = 60\)
=> \(B = 60 - 3M\)

Now multiply with individual prices: total cost is 4200$

\(M * 30 + (60 - 3M) * 50 + 2M * 120 = 4200\)
=> \(120M + 3000 = 4200\)
=> \(M = 1200 / 120 = 10\)

Now, using M to get B and F:
\(B = 60 - (3 * 10) = 30\)
\(F = 2M = 20\)

Question: B / F (the ratio of the number of blenders sold to the number of food processors sold?)

\(B / F = 30 / 20 = \) 3 / 2
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Re: A dealer sold a total of 60 of the three appliances listed in the tabl [#permalink]
this took me 3.5 minutes to get it right,

is there a shorter more logical approach to this?
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Re: A dealer sold a total of 60 of the three appliances listed in the tabl [#permalink]
Bunuel

A dealer sold a total of 60 of the three appliances listed in the table above for a total of $4,200. If the dealer sold twice as many food processors as mixers, what was the ratio of the number of blenders sold to the number of food processors sold?

A. 3/2
B. 4/3
C. 6/7
D. 5/12
E. 1/3

PS20379


Attachment:
1.png

total appliances = 60

Twice the number of food processers were sold compared to the number of mixers

let 2x = number of food processers sold
let x = number of mixers sold

We can create the following equation:

\(120(2x) + 30x + 50(60-3x) = 4,200\)

\(240x + 30x + 3,000 - 150x = 4,200\)

\(120x = 1,200\)

\(x = 10\)

number of blenders sold = \(60-3(10) = 30\)

number of food processors sold = \(2x = 20\)

\(\frac{30}{20} = \frac{3}{2}\)

Answer is A.
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A dealer sold a total of 60 of the three appliances listed in the tabl [#permalink]
sold twice as many food processors as mixers

I got confused in the statement:-

P: food processor m: mixer

I did the problem with 2p = m instead of p = 2m and got the answer negative.

What is the difference between

sold twice as many food processors as mixers, and sold food processors twice as many as mixers.

Is there any concept clearing blog on the language?

Bunuel VeritasKarishma bb chetan2u
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Re: A dealer sold a total of 60 of the three appliances listed in the tabl [#permalink]
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rsrighosh
sold twice as many food processors as mixers

I got confused in the statement:-

P: food processor m: mixer

I did the problem with 2p = m instead of p = 2m and got the answer negative.

What is the difference between

sold twice as many food processors as mixers, and sold food processors twice as many as mixers.

Is there any concept clearing blog on the language?

Bunuel VeritasKarishma bb chetan2u

Twice as many A as B means number of As is more.
If you get confused, try to take a simple example:
My height is twice as much as his - am I taller or is he? I, right?
So in twice as many A, number of As is more.

This means A = 2B
When you double B, you get the number of A.
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Re: A dealer sold a total of 60 of the three appliances listed in the tabl [#permalink]
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Video solution from Quant Reasoning starts at 22:35
Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1
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Re: A dealer sold a total of 60 of the three appliances listed in the tabl [#permalink]
BrentGMATPrepNow
Bunuel

A dealer sold a total of 60 of the three appliances listed in the table above for a total of $4,200. If the dealer sold twice as many food processors as mixers, what was the ratio of the number of blenders sold to the number of food processors sold?

A. 3/2
B. 4/3
C. 6/7
D. 5/12
E. 1/3
PS20379
Attachment:
1.png

The dealer sold twice as many food processors as mixers.
Let M = the number of mixers has sold
So, 2M = the number of the food processors sold

The dealer sold a total of 60 of the three appliance
M + 2M = 3M
So, 3M represents the total number of mixers and food processors sold.
Since 60 appliances were sold in total, 60 - 3M = the number of blenders sold

The dealer sold everything for a total of $4,200
We get: (30)(M) + (120)(2M) + (50)(60 - 3M) = 4,200
Simplify: 30M + 240M + 3000 - 150M = 4200
Simplify: 130M + 3000 = 4200
Subtract 3000 from both sides: 120M = 1200
Divide both sides by 120 to get: M = 10

So, the dealer sold 10 mixers
This means the dealer sold 20 food processors
And the dealer sold 30 food processors

Ratio of blenders sold to food processors sold = 30/20 = 3/2

Answer: A

Cheers,
Brent


@BrentGMATPrepNowI did try solving the above using algebra however I am not sure where am I going wrong:

A dealer sold a total of 60 of the three appliances listed in the table above for a total of $4,200.

M + B + F = 60

30M + 50B + 120F = 4200

3M + 5B +12F = 420

If the dealer sold twice as many food processors as mixers

F = 2M ; M = F/2

3(F/2) + 5B + 12F = 420

3F + 10B + 24F = 840

27F + 10B = 840

27F = 840 - 10B

F = [840 - 10B]/27

If B = 3 ; F = 30

B/F = 3/30 --> 1/10
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A dealer sold a total of 60 of the three appliances listed in the tabl [#permalink]
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Here's a visual that should help.­

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Re: A dealer sold a total of 60 of the three appliances listed in the tabl [#permalink]
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­Pretty stratiforward mixture:

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Re: A dealer sold a total of 60 of the three appliances listed in the tabl [#permalink]
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