a certain sum of money 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 £2.10. how much is the sum of money
If the total is x, then we know that
2/5 x + 1/4 x + 2.10 = x
Now just solve for x
x - 2/5x - 1/4x = 2.1
x - 0.4x - 0.25x = 2.1
x - 0.65x = 2.1
0.35x = 2.1
x = 2.1/0.35
Let's assume the total sum of money is "x" pounds.
According to the given information:
- One brother gets 2/5 of the sum, which is (2/5)x pounds.
- Another brother gets 1/4 of the sum, which is (1/4)x pounds.
- The third brother gets £2.10.
We can set up the equation:
(2/5)x + (1/4)x + £2.10 = x
To simplify the equation, we need to convert pounds to a decimal value. Assuming there are 100 pence in a pound, £2.10 would be equal to 210 pence.
Now we solve the equation:
(2/5)x + (1/4)x + 210 = x
To solve for x, we can multiply the equation by the least common denominator (LCD) of 5 and 4, which is 20:
20 * (2/5)x + 20 * (1/4)x + 20 * 210 = 20x
This simplifies to:
8x + 5x + 4200 = 20x
Combining like terms:
13x + 4200 = 20x
Subtracting 13x from both sides:
4200 = 7x
Now, divide both sides by 7 to solve for x:
x = 4200 / 7
x = £600
Therefore, the sum of money is £600.
To find the total sum of money, we need to add up the amounts each brother receives.
Let's represent the unknown sum of money as "x".
According to the information given:
- One brother receives 2/5 of the total sum, which can be calculated as (2/5) * x.
- Another brother receives 1/4 of the total sum, which can be calculated as (1/4) * x.
- The third brother receives £2.10.
So, we can set up the equation: (2/5)x + (1/4)x + £2.10 = x.
To solve this equation, we need to get rid of the fractions. We can do this by finding a common denominator, which in this case is 20.
Multiplying throughout the equation by 20, we get: 8x + 5x + 42 = 20x.
Combining like terms, we have: 13x + 42 = 20x.
Next, we'll isolate the variable by subtracting 13x from both sides of the equation: 42 = 7x.
Finally, dividing both sides of the equation by 7, we find that x = 6.
Therefore, the total sum of money is £6.