Opinion on a word problem

[BigBeachBanana]

An antique store buys its good from walk-in customers. For a particular chair, the antique store charges what it paid the customer plus 150%. During a sale, the antique store charged what it paid the customer plus 50% instead. If the sale price of the chair was $75, what was the price of the chair before the sale?

This question was taken from an SAT prep book. Those who attempted this question often get the answer wrong. I'm interested in your interpretation of the question and your solution. To remain unbiased, I will not share the book's solution upfront.

 

[Deleted member 4993]

This question was taken from an SAT prep book. Those who attempted this question often get the answer wrong. I'm interested in your interpretation of the question and your solution. To remain unbiased, I will not share the book's solution upfront.

Assume that the store paid the customer = B

The asking price of the chair before sale = 2.5 * B....................

The asking price of the chair during sale = 1.5 * B = 75 → B = 50

The asking price of the chair before sale = 2.5 * B = 2.5 *50 = 125 ...................... answer

 

[Cubist]

what was the price of the chair before the sale?

Spoiler: my opinion

This question is ambiguous IMO, since the chair had two prices before the final sale. There's the price that the shop paid for the chair, $50. There's also the price that the store wanted to sell chair for $125. However, I think this latter price is what the book is after - otherwise the question would contain redundant information.

 

[Deleted member 4993]

Spoiler: my opinion

This question is ambiguous IMO, since the chair had two prices before the final sale. There's the price that the shop paid for the chair, $50. There's also the price that the store wanted to sell chair for $125. However, I think this latter price is what the book is after - otherwise the question would contain redundant information.

the price that the shop paid for the chair

That price is expressed in the "question" as what it paid the customer.

 

[Steven G]

An antique store buys its good from walk-in customers. For a particular chair, the antique store charges what it paid the customer plus 150%. During a sale, the antique store charged what it paid the customer plus 50% instead. If the sale price of the chair was $75, what was the price of the chair before the sale?

Let x be the price the store paid for the chair.
Normally the chair sells in the store for 2.5x.
The sale price will be 1.5x=$75
So x=$50 and the chair normally sells for $125

 

[Otis]

the chair had two prices before the final sale.

Spoiler

But, technically reading, the exercise statement doesn't refer to the $50 paid by the shop as a "price". The English is clear enough for me (prices are what the shop asks). However, the presentation of the scenario is somewhat twisty. The author did the same thing with "customer", using that noun to describe the person who sold the chair to the shop and then implying that another customer purchases the chair for $75. It took me a few moments to decide that was irrelevant to the exercise at hand. Definitely not a nice wording for students who may lack fluency with English.

[imath]\;[/imath]

 

[Cubist]

Spoiler: dictionary definition of price

1. the amount of money expected, required, or given in payment for something.

(...according to the great Google anyhow )

the antique store charges what it paid the customer plus 150% ...

 

[Otis]

… before the sale?

Spoiler

That's "the sale", as in "a period of lowered prices". It's clear to me that the exercise asks for the pre-sale price, but I certainly would have worded that exercise differently!

My work matches the method posted by Subhotosh and Steven.

?

[imath]\;[/imath]

 

[Steven G]

That's "the sale", as in "a period of lowered prices". It's clear to me that the exercise asks for the pre-sale price, but I certainly would have worded that exercise differently!

My work matches the method posted by Subhotosh and Steven.

?

[imath]\;[/imath]

Somehow SK stole my answer. It is exactly the same. Being a Super Moderator he placed his post ahead of mine. I don't care that I posted my post after him.

 

[Cubist]

Spoiler: my opinion

This seems to be escalating out of proportion ?. Please note that I stated in post#3 that, "I think this latter price (of $125) is what the book is after". Therefore I actually agree with SK, Steven, and yourself on the answer. Hmmm, perhaps the argument is whether or not the question is ambiguous For me, their use of the word "before" isn't specific enough, in time, to be completely unambiguous. I would have needed, "immediately before the sale" or some other improved way to state the problem. I guessed the intent was $125 from the extra supplied information which wouldn't have been required otherwise.

Anyway - we would have all got 100% on this - I think - unless BBB surprises us with something unexpected

 

[tri]

It is possible for some to miss charges paid + 150% or 50% (during sale) and incorrectly take 150% or 50% (during sale) instead.

Spoiler

75 = p + (0.5)p [p=price paid to walk-in customer]
Price before sale = p + (1.5)p = $125
It is unknown how many prices the chair had before the sale or before arriving at the antique store (given the antique nature of goods sold at an antique store).

 

[Steven G]

This question was taken from an SAT prep book. Those who attempted this question often get the answer wrong. I'm interested in your interpretation of the question and your solution. To remain unbiased, I will not share the book's solution upfront.

....so what are the two answers that usually come up. Are we all wrong? That would be sad. Then again, we can then all meet on the same corner and have a party.

 

[BigBeachBanana]

....so what are the two answers that usually come up. Are we all wrong? That would be sad. Then again, we can then all meet on the same corner and have a party.

Fortunate for you, you've answered the question correctly as intended per the book.
I think the main source of the confusion, as @Cubist pointed out, students often interpret the question as having 2 prices before the final sale. This is actually a multiple choice question where both $50 and $125 are included, and they often choose the $50 choice. Additionally, I think @Otis made a valid point about the language isn't clear enough. It made the transactions between all the parties a bit unclear.
Keep in mind this was an SAT question that students are supposed to answer under time pressure.

Appreciate all of your time and opinions.