A certain is to be shared among three brothers ,one of them gets 2/5 of it,another gets 1/4 of it and the third one gets #2.10k. How much is the sum of money?
(2/5)x + (1/4)x + 2.10 = x
(8/20)x + (5/20)x + 2.10 = x
(13/20)x + 2.10 = x
2.10 = 7/20x
2.10 / (7/20) = x
2.10 * (20/7) = x
42/7 = 6 = x
It looks like the original was 6K.
(2/5)s + (1/4)s = (8/20 +5/20)s
= (13/20)s
so
(7/20)s = 2.10
To find the total sum of money, we need to add up the shares of each brother. Let's break it down step by step:
1. Let's assign variables to represent the shares of each brother.
- Let x be the total amount of money.
2. The first brother receives 2/5 of the total amount.
- His share is (2/5) * x.
3. The second brother receives 1/4 of the total amount.
- His share is (1/4) * x.
4. The third brother receives #2.10k.
- His share is #2.10k.
5. We can now set up an equation to represent the sum of their shares.
- (2/5) * x + (1/4) * x + #2.10k = x (the total amount)
6. Let's solve the equation to find the value of x.
- Multiply each fraction by the least common denominator (20) to remove the denominators:
(2/5) * x + (1/4) * x + #2.10k = x
8x/20 + 5x/20 + #2.10k = x
(8x + 5x)/20 + #2.10k = x
(13x/20) + #2.10k = x
- Move the terms containing x to one side of the equation:
(13x/20) - x = -#2.10k
13x/20 - 20x/20 = -#2.10k
(13x - 20x)/20 = -#2.10k
-7x/20 = -#2.10k
- Multiply both sides of the equation by -20 to eliminate the fraction:
-20 * (-7x/20) = -20 * (-#2.10k)
7x = #42k
- Divide both sides of the equation by 7 to solve for x:
7x/7 = #42k/7
x = #6k
The total sum of money is #6,000.