Otieno, Leila, Rotich and Furaha shared $840. Otieno got twice as much as Leila. Leila got three times as much as Rotich while Rotich got half of what Furaha got. What was the difference between Otieno's share and Furaha's share?
If the four got amounts a,b,c,d respectively, then
a = 2b
b = 3c
c = d/2
a+b+c+d = 840
a-d = 280
Well, it looks like there's a bit of a money circus going on here! Let's break it down. If we let Furaha's share be x, then we know that Rotich got half of that, which means Rotich got x/2. Leila, on the other hand, got three times what Rotich got, so Leila got 3(x/2) or 3x/2. And finally, Otieno got twice as much as Leila, so Otieno got 2(3x/2) or 3x.
Now, we know that the sum of their shares is $840, so we can set up an equation:
x + x/2 + 3x/2 + 3x = 840.
If we simplify that, we get 4x + 5x = 840, which further simplifies to 9x = 840.
Solving for x, we find that x = 840/9 = 93.33.
So, Furaha's share is approximately $93.33.
Otieno's share is 3x, which is 3 * 93.33 = $279.99.
The difference between Otieno's share and Furaha's share is $279.99 - $93.33 = $186.66.
That's quite a chunk of change!
Let's solve the problem step by step:
Step 1: Assign variables
Let's assume:
Leila's share = L
Rotich's share = R
Furaha's share = F
Otieno's share = O
Step 2: Write the given equations
Based on the given information, we can write the equations as follows:
O + L + R + F = 840 (equation 1)
O = 2L (equation 2)
L = 3R (equation 3)
R = 0.5F (equation 4)
Step 3: Solve the equations
Using equations 2 and 3, we can substitute into equation 1:
2L + L + L/3 + 0.5F + F = 840
Multiplying through by 3 to eliminate the fraction, we get:
6L + 3L + L + 1.5F + 3F = 2520
Combining like terms, we have:
10L + 4.5F = 2520 (equation 5)
Using equations 2 and 4, we can substitute into equation 5:
10(2L) + 4.5(2F) = 2520
20L + 9F = 2520 (equation 6)
Step 4: Solve the resulting equations
Now we have two equations:
10L + 4.5F = 2520 (equation 5)
20L + 9F = 2520 (equation 6)
Multiplying equation 5 by 2, we get:
20L + 9F = 5040
Subtracting equation 6 from this result:
20L + 9F - (20L + 9F) = 5040 - 2520
0 = 2520
Since this is contradictory, there is no solution to the system of equations. This means there is an error or inconsistency in the given information.
Please double-check the problem statement and provide the correct information.
To find the difference between Otieno's share and Furaha's share, we first need to determine the amounts that each person received. Let's break down the information given:
Let's assume Rotich's share to be x.
- Leila got three times as much as Rotich; therefore, Leila's share is 3x.
- Otieno got twice as much as Leila; therefore, Otieno's share is 2 * 3x = 6x.
- Rotich got half of what Furaha got; therefore, Furaha's share is 2x.
Now we can set up an equation to find the value of x:
x + 3x + 6x + 2x = 840
Combining like terms, we have:
12x = 840
Dividing both sides of the equation by 12, we get:
x = 70
Now we can find the value of Otieno's and Furaha's shares:
Otieno's share = 6x = 6 * 70 = 420
Furaha's share = 2x = 2 * 70 = 140
The difference between Otieno's share and Furaha's share is:
420 - 140 = 280
Therefore, the difference between Otieno's share and Furaha's share is $280.