Solution:

$6 for red sponges = 1 sponges
$87 for yellow sponges = 29 sponges
$7 for blue sponges = 70 sponges

Explanation:
a = red sponges
b = yellow sponges
c = blue sponges

Now using a simple expression:
A + b + c = 100
6a + 3b + 0.1c = 100

Now if we multiply the first equation by 6 and then 3 and then subtracting the two equations, we will be able to get two more equations:

6a + 6b + 6c = 600
3a + 3b + 3c = 300

3b = 500 - 5.9c
3a = 2.9c - 200

Now if you are wondering how will we solve three variables using just two equations, we have to tell you that a and b are non-negative integers. Thus, if 3b >/= 0, then 500 - 5.9c >/= 0.
Using this, c Also, if 3a >/= 0, then 2.9c - 200 > 0. This implies that c >/= 68.97.

But buying the blue sponges is the only way to spend in fraction thus the number of blue sponges that we buy must cost an even dollar amount. Now if you consider the expressions, there can be only two numbers we can buy between 68.97 and 84.75 that satisfies the given condition i.e. 70 and 80.

Let's say that we replace c by 80 in the last two expressions that we have formed above, a will equal to 10.67 and b will equal to 9.33. However, the values of a and b must be an integer and not fraction. Therefore, c can't be 80.

Let us now replace c with 70. After solving the expressions, we will obtain a as 1 and b as 29.

Thus here are the amounts that must be used to buy:
$6 for red sponges = 1 sponges
$87 for yellow sponges = 29 sponges
$7 for blue sponges = 70 sponges

Solution:

Step 5 is invalid, because we are dividing by (x-y), and since x=y, we are thus dividing by 0. This is an invalid mathematical operation (division by 0), and so by not following basic mathematical rules

Solution:

Since the knife was in her hand which implies that she was planning to kill her husband "Inspector Montalbano".

Solution:

This is more of a philosophical question than being a riddle or a puzzle. The action of Brian directly led to the result which is the death of Chris. Thus he murdered Chris. In a sense, Chris died due to the lack of water. It is the circumstances that ultimately led to his death.

Solution:

The man asked the king that he wanted to die of old age.

Solution:

457730 * 4 = 1830920
(DOLLAR * 4 = QUARTER)

Solution:

Are you Thorgan

Explanation:
Below will be the reply of three brothers:
Eden: No (speaks truth)
Thorgan: No (speaks lie)
Kylian: Yes (speaks lie)

Therefore if its Kylian then only you will get a reply as "Yes" and then you ask for your money.

Solution:

Hhe hung herself using big Ice slabs , which are now now melted and hence puddle of water.

Solution:

Kid1, he was left with one rock.

Solution:

Let us assume that all of them are standing on the X shore and they have to travel to the Y shore.

X = mother, first daughter, second daughter, father, first son, second son, maid and dog
Y = None

Maid and dog go first and maid returns back
X = mother, first daughter, second daughter, father, first son, second son and maid
Y = dog

Maid and first son go and maid returns with dog
X = mother, first daughter, second daughter, father, second son, maid and dog
Y = first son

Father and second son go and father returns back
X = mother, first daughter, second daughter, father, maid and dog
Y = first son and second son

Mother and father go and mother comes back
X = mother, first daughter, second daughter, maid and dog
Y = father, first son and second son

Maid and Dog go and Father returns back
X = mother, first daughter, second daughter and father
Y = first son, second son, maid and dog

Father and Mother go and mother comes back
X = mother, first daughter and second daughter
Y = father, first son, second son, maid and dog

Mother and first daughter go and maid comes back with dog
X = second daughter, maid and dog
Y = mother, first daughter, father, first son and second son

Maid and second daughter go and maid comes back
X = Maid and dog
Y = mother, first daughter, second daughter, father, first son and second son

Maid and dog go
X= none
Y = mother, first daughter, second daughter, father, first son, second son, maid and dog

Thus everyone has reached the other end.

Solution:

The last marble will be yellow.

Since marbles can only be taken out in pairs and you started off with an odd number of yellows there is always going to be one yellow left over that you'll keep putting back in the box until it's left on it's own.