Math Challenge 21

Some math questions are simple and can be answered easily.

See this math challenge 20 and its answer in the comment.

But a twist of the questioning will and can make it more challenging without changing the math expression.

Below is one:

Base on math challenge 20, if all unknowns CANNOT be repeated, what are they?
Again they are integers and below 10.

Enjoy the math thrill answering this.

Merry Christmas!
^.^

Math Challenge 20

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Can anyone come out the answers for A, B, C and D in the below math expression?

A² + B² + 2C² = D²

The rule is that the unknowns are all integers and below 10.

Happy trying, and
don't forget that maths is interesting!

:-)

Percentage | Common Mistake

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Percentage problems can be tricky at times when you are careless.

Let's us look at one maths word problem related to it.

Question:
There are 3 persons, John, Mary and Jane.
John is richer than Mary by 10%, and Mary is richer than Jane by 20%.
Is John richer than Jane by (10 + 20)% = 30% ?

Most students, upon quick thinking, will acknowledge that 30% is the correct answer.

Is it so?

To verify the answer, let us assume that Jane has $1000.
As such, Mary will have (100+20)% of $1000 = 1.2 x $1000 = $1200.
John is then 1.1 x $1200 = $1320 richer than Jane ==> By 32%.

If 30% is correct, we should get 1.3 X $1000 = $1300.

The latter number (dollar) is not the same as the first worked out solution.
Why?

Mistake in understanding what is percentage:
To assume that John is 10% + 20% richer than Jane is incorrect.
This is due to the fact that percentage has to take a common reference for this to be correct.

In the word problem, the percentages of comparison are not to a common reference.
The first one is to Mary, while the next is to Jane.

These made the denominator of the ratio different.
Thus adding the percentage up is a mistake, and an easy one too!

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