Oliver, Daniel and Henry shared a sum of money together. Oliver and Daniel received 3/4 of the total amount of money. Daniel and Henry received 3/5 of the total amount of money. If Oliver received $36 more than Henry, how much was the total sum of money?
O + D = (3/4) M
D + H = (3/5) M
O = H + 36
================
H + 36 + D = (3/4) M
H + D = (3/5) M
-------------------------- subtract
36 = (3/4 - 3/5) M = (15-12) M /20 = 3 M /20
M = 12*20 = 240
Useless
Let's assume the total sum of money to be "x".
According to the given information, Oliver and Daniel received 3/4 of the total sum of money, which means their share is (3/4) * x.
Similarly, Daniel and Henry received 3/5 of the total sum of money, which means their share is (3/5) * x.
We are also given that Oliver received $36 more than Henry, so we can write an equation based on that:
Oliver's share = Henry's share + $36
(3/4) * x = (3/5) * x + $36
To solve this equation, we can cross multiply:
5 * (3/4) * x = 4 * (3/5) * x + 4 * $36
15x/4 = 12x/5 + $144
Now, we can simplify the equation by multiplying both sides by 20 (common denominator for 4 and 5):
5 * 15x = 4 * 12x + 20 * $144
75x = 48x + $2880
Subtracting 48x from both sides, we get:
75x - 48x = $2880
27x = $2880
Dividing both sides by 27, we find:
x = $2880 / 27
x ≈ $106.67
Hence, the total sum of money is approximately $106.67.