M31-18

Question

The ratio of red boxes to blue boxes in a certain warehouse is 12 to 25. If the number of red boxes were doubled and the number of blue boxes was increased by 150, the ratio would be halved. How many total boxes are in the warehouse?

A. 37
B. 74
C. 111
D. 148
E. 244

Show Answer

Official Answer

B

A. 37
B. 74
C. 111
D. 148
E. 244

Bunuel · Answer

Official Solution:

The ratio of red boxes to blue boxes in a certain warehouse is 12 to 25. If the number of red boxes were doubled and the number of blue boxes was increased by 150, the ratio would be halved. How many total boxes are in the warehouse?

A. 37
B. 74
C. 111
D. 148
E. 244

Show Answer

Official Answer

B

A. 37
B. 74
C. 111
D. 148
E. 244

The ratio of red boxes to blue boxes in a certain warehouse is 12 to 25 -  Red:Blue = 12x:25x .
 
If the number of red boxes were doubled and the number of blue boxes was increased by 150, the ratio would be halved -  \frac{(2*12x)}{(25x + 150)} = \frac{1}{2}*\frac{12}{25} , which gives  x = 2 .
 
Total boxes =  Red + Blue = 12x + 25x = 37x = 74 .

Answer: B

wmichaelxie · Answer

Quick question - how do we know if they're asking for the "before" count or "after" count? Could a rule be that anytime they pose the question as a hypothetical, the question is asking for the number before any changes?

Bunuel · Answer

The question asks  "How many total boxes are in the warehouse NOW" ? The hypothetical change is given to calculate the current number, for which we know that the ratio of red boxes to blue boxes is 12 to 25.

landoro15 · Answer

Wouldn't that be specified in the problem then? I was just assuming that the question was asking for the amount of total boxes given the increase - would it be possible to solve for that? I was getting 259 for that and was very confused to how that wasn't an answer choice (lol)

One other question -- how did you algebraicially solve for x? I set up the equation in the right way, but cannot seem to get x=2.

One other question -- how did you algebraicially solve for x? I set up the equation in the right way, but cannot seem to get x=2.

Bunuel · Answer

1. What should be specified? The question is mathematically and grammatically correct:
The ratio of red boxes to blue boxes in a certain warehouse  IS  12 to 25.  IF  the number of the red boxes were doubled and the number of blue boxes were increased by 150 the ratio would be halved. How many total boxes  ARE  in the warehouse? ( ARE  not  WOULD BE )

2.  \frac{(2*12x)}{(25x + 150)} = \frac{1}{2}*\frac{12}{25}

\frac{(2x)}{(25x + 150)} = \frac{1}{50}

100x = 25x + 150

75x = 150

x = 2 .

Hope it helps.

okrahulnambiar · Answer

I did not understand as to how when we setup the equation to solve, the RHS did not comprise of 12x/25x instead of 12/25. We do need to be mindful that the equation still is an unknown and not fixed with two constants.

Bunuel · Answer

\frac{(2*12x)}{(25x + 150)} = \frac{1}{2}*\frac{12}{25}

In the left-hand side, with x, we have the number of blue and red boxes in the numerator and denominator respectively. However, on the right-hand side, we have the ratio. Also, note that if we put 12x/(25x), x would cancel out, still leaving us with 12/25.

Hope it helps.

Bunuel · Answer

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

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M31-18

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