Explanation

Find the number of TV sets sold by Store R:

Table: 40 in stock
Graph: 50% sold

50% of 40 = \(0.50 \times 40 = 20\)

Find the number of TV sets sold by Store T:

Table: 50 in stock
Graph: 90% sold
90% of 50 = \(0.90 \times 50 = 45\)

Use the percent change formula to find the approximate percent decrease:

Percent change = decrease \div original number \times 100

\((45 - 20) \div 45 \times 100 = 25 \div 45 \times 100 = 0.555 \times 100 = 55.5%\)

Hence option B is correct.
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Sandy,

I'm sure your answer is right, but it's not clear to me why we wouldn't find the percentage difference instead of finding the percentage change. I was looking at mathisfun's page on Percentage Difference and on it was the following passage:

"When Should it be Used?

Percentage Difference is used when both values mean the same kind of thing (for example the heights of two people).

But if there is an old value and a new value, we should use Percentage Change
Or if there is an approximate value and an exact value, we should use Percentage Error

"
To me it seems like we are comparing two values of the same type, like height, not finding a change. So, it seems like percentage difference would make more sense. It's obviously wrong as the answer I got for percentage difference is not even close to one of the available answers. So, my question is why? Why does it make more sense to use percentage change in this case?

Percent change

Percent Change = New Value − Old Value|Old Value| × 100%

The Percentage Difference is when you divide by the Average of The Two Values

Percentage Difference = | First Value − Second Value(First Value + Second Value)/2 | × 100%


here you do not have this scenario.

here, we have to compare the difference between the two (25) compare to the television sets sold by T

25/45 which is roughly 55.5 %

Answer choice B is the closest.

Hope now is more clear to you.

Regards

PS: sandy's explanation is really top notch. Almost a luxury explanation. It has all you need to tackle the question in the most efficient way.

As Carcass pointed out the key factor for evaluating percentages is the Base.

I.E. the denominator of the fraction. Now whenever there is time line in the question the old value is in the denominator and and the new value is in the numerator.

It is very important to understand this concept. Percentages are not your friend.


For example, lets say You have 10kg of Orange which is 99 percent water by weight. They have been outside for a few days and some water evaporated so now they are 98% water by weight. What is the weight of oranges?

Some people would calculate.

The weight of Orange = 10kg weight of water= 9.9 kg.

New weight of water = 9.8 kg

However, this is wrong. because 98% water is based on new weight of oranges.

The correct way to solve this is finding the new weight of oranges. Say \(x\) amount of water get evaporated from 10 kgs of oranges.

\(\frac{9.9 -x}{10 -x}= 0.98\) or

\(9.9 - x = 9.8 - 0.98x\) or

\(9.9-9.8=0.02x\) or

\(x= 5\)

So for one percent change in mass of water the amount of water evaporated is 5 ks half of the entire orange.
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Hi, i still do not get which number to be the denominator. In this question i put 20 as the denominator instead of 45, which gives me the answer E). I am still not clear how to differentiate which is the original, in this case, i do not know if it's store T or Store R, it is confusing. Pease help.

Order matters. When you change from one value to another and want the percentage change, it matters which value was the starting value.

In this case is a % decrease and still, the first value is 45. It is a rule.

However, if you do wanna a % increase the starting value is STILL the first.

Example: 400 to 500. The difference is still 100 and the starting value is 400. 1/4 = 25 % increase

When in doubt simplify it as ..

R is what % less than T....
What comes after THAN is you denominator

Say it was T is what % greater than R..
What comes after THAN again is the base
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I would like to add that anything written after "Than" comes in denominator.
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