A dealer sold a total of 60 of the three appliances listed in the tabl

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

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

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

Posted from my mobile device
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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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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

this took me 3.5 minutes to get it right,

is there a shorter more logical approach to this?

kiranbhasker Not really, you have to do a lot of small steps accurately. Ideally, you are very organized, and fluent and confident on each step. The chart shown below can help with organization. This is a particularly long problem, as we can see from the average correct time of 2:54.

If done with little hesitation, this can be done with the method below in under 2:00. (However, you have to be careful to avoid a careless algebra error, and I had done the problem once before).

I encourage you to re-do it, with a competitive mindset to see how much you can improve your time, while still retaining accuracy.

Many people have the habit of using an RT = W or RT = D chart, for work and rate problems. To be more organized and reduce hesitation in our process, we can use a similar chart, for PQ = R (Price * Quantity = Revenue).

We also want to be very fluent in translating "twice as many food processors as mixers". It's common to mix this up and do it backwards. Double check -- what are there more of? More food processors -- so put "2x" in the "F" row, and "x" in the "M" row (see brown writing below; MGMAT calls this the "Unknown Multiplier" method, for ratios)

It can also be helpful to "rephrase" in advance what they are asking for -- this habit helps us prevent the careless error of answering the wrong question. (see green writing below).

In the blue writing below, we subtract the values above and below from the total quantity of 60.

In the purple writing on the right side, we turn the revenue column into an equation -- I did the 240x + 30x - 150x in my head and simplified carefully, to save a bit of writing. I like to cross things off on both sides of the equation, instead of writing a new line for each algebra step (Reason: I find that sometimes additional steps introduce additional potential errors, such as copying something incorrectly from the previous line. Caution: you need to practice this "cross-off" method and make sure you are aware of what's crossed off and what isn't.)

Please let me know if you have any questions or comments, thanks!

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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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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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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Video solution from Quant Reasoning starts at 22:35
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@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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