lbrahim spends a quarter of his salary on school fees one ninth on water and electricity bills thirds of the remainder on house up keep and saves the rest .The difference between what he saves and the amount he spends on house up keep is Kshs. 10,350. Calculate Ibrahim's monthly salary.
just thirds?
Let's assume Ibrahim's monthly salary as "x" Kshs.
He spends a quarter of his salary on school fees, which is (1/4)x Kshs.
He spends one-ninth of his salary on water and electricity bills, which is (1/9)x Kshs.
The remainder of his salary after deducting school fees and bills is:
x - (1/4)x - (1/9)x
Now, he spends one-third of the remainder on house upkeep, which is (1/3)(x - (1/4)x - (1/9)x) Kshs.
The amount he saves is the difference between what he saves and the amount he spends on house upkeep, which is:
[(1 - 1/3) * (x - (1/4)x - (1/9)x)] - [(1/3)(x - (1/4)x - (1/9)x)] = Kshs. 10,350
Simplifying the equation:
[(2/3) * (x - (1/4)x - (1/9)x)] - [(1/3)(x - (1/4)x - (1/9)x)] = 10,350
Now, let's solve this equation step-by-step.
Step 1: Expand the equation:
[(2/3)x - (2/3)(1/4)x - (2/3)(1/9)x] - [(1/3)x + (1/3)(1/4)x + (1/3)(1/9)x] = 10,350
Step 2: Combine like terms:
[(2/3)x - (1/6)x - (1/9)x] - [(1/3)x - (1/12)x - (1/27)x] = 10,350
Step 3: Calculate the fractions:
[(8/12)x - (2/12)x - (1/12)x] - [(3/9)x - (1/12)x - (1/27)x] = 10,350
Step 4: Combine like terms:
[(5/12)x] - [(7/36)x] = 10,350
Step 5: Simplify the equation:
[(15/36)x] = 10,350
Step 6: Multiply both sides of the equation by 36/15 to isolate x:
x = (10,350 * 36) / 15
x = 24,840
Therefore, Ibrahim's monthly salary is Kshs. 24,840.
To solve this problem, we can break it down step by step and use algebra to find the monthly salary of Ibrahim.
1. Let's assume Ibrahim's monthly salary is "x" Kshs.
2. According to the information given, Ibrahim spends a quarter (1/4) of his salary on school fees. So, his expenses on school fees would be: (1/4) * x = x/4 Kshs.
3. He also spends one-ninth (1/9) of his salary on water and electricity bills. So, his expenses on water and electricity bills would be: (1/9) * x = x/9 Kshs.
4. The remainder after paying school fees and water/electricity bills is the amount that can be used for house upkeep and savings. So, the remainder would be: x - (x/4) - (x/9).
5. According to the given information, Ibrahim spends one-third (1/3) of the remainder on house upkeep. So, his expenses on house upkeep would be: (1/3) * (x - (x/4) - (x/9)) = (1/3) * ((36x - 9x - 4x)/(36)) = 11x/36 Kshs.
6. Ibrahim saves the rest of the remainder, which is the monthly salary minus the expenses on school fees, water/electricity bills, and house upkeep. So, the amount he saves would be: (x - (x/4) - (x/9)) - (11x/36).
7. The problem states that the difference between what Ibrahim saves and the amount he spends on house upkeep is 10,350 Kshs. Therefore, we can set up the following equation: [(x - (x/4) - (x/9)) - (11x/36)] - (11x/36) = 10,350.
8. Now, we can solve the equation for x, which represents Ibrahim's monthly salary.
Let's solve the equation step by step:
[(x - (x/4) - (x/9)) - (11x/36)] - (11x/36) = 10,350.
[(x - (9x/36) - (4x/36)) - (11x/36)] - (11x/36) = 10,350.
[(x - (9x + 4x)/36) - (11x/36)] - (11x/36) = 10,350.
[(x - (13x)/36) - (11x/36)] - (11x/36) = 10,350.
[(36x - 13x - 11x)/36] - (11x/36) = 10,350.
[(36x - 24x)/36] - (11x/36) = 10,350.
(12x/36) - (11x/36) = 10,350.
x/36 = 10,350.
To isolate x, multiply both sides of the equation by 36:
x = 10,350 * 36.
Calculating the right-hand side of the equation:
x = 372,600 Kshs.
Therefore, Ibrahim's monthly salary is 372,600 Kshs.