.Kinyua spent 1/4 of his net January salary on school fees. He spent 1/4 of the remainder on
electricity and water bills. He spent 1/9 of what remained on transport. If he finally has
sh.8400, calculate
a) His total January salary
b) Money spent on school fees
c) Money spent on transport
d) Money spent on electricity and water bills
Net salary = $x.
school fees: x/4. Remainder = 3x/4.
electricity: 1/4 * 3x/4 = 3x/16. remainder = 3x/4-3x/16 = 9x/16.
transportation: 1/9 * 9x/16 = x/16. remainder = 9x/16-x/16 = 8x/16.
a. 8x/16 = 8400
X = 16,800.
b. x/4 =
c. x/16 =
d. 3x/16 =
d.3x/16=44,800✓.
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a) Oh boy, this sounds like a math problem! Alright, let's solve it. If Kinyua ended up with sh.8400 after all his expenses, that means sh.8400 is what remains after spending on transport. Let's work our way backward! Since he spent 1/9 of what remained on transport, that means 1 - 1/9 = 8/9 is what remained after spending on electricity and water bills. And if he spent 1/4 of what remained on electricity and water bills, that means 1 - 1/4 = 3/4 is what remained after spending on school fees. Phew! Now, if 3/4 is what remained after spending on school fees, then 3/4 * (8/9) * (8400) = sh.8400. Solve that equation and you'll find the total January salary!
b) Since we already know the total January salary from the previous calculation, we can multiply it by 1/4 to find out how much was spent on school fees. Easy-peasy!
c) To find the money spent on transport, we multiply the total January salary by 1/4 (school fees) by 1/9 (transport). Et voilà!
d) Finally, to determine the money spent on electricity and water bills, we multiply the total January salary by 1/4 (school fees) and subtract the money spent on transport and what remains. Got it?
To solve this problem, we'll need to work backwards from the final amount of sh.8400.
Let's begin:
a) To find the total January salary, we'll start with the final amount of sh.8400 and work backwards. We know that sh.8400 is what remains after deducting amounts spent on transport. So, let's calculate the amount before any deductions:
Total January salary = sh.8400 ÷ (1 - 1/9) = sh.8400 ÷ (8/9) = sh.9450
Therefore, Kinyua's total January salary is sh.9450.
b) To find the money spent on school fees, we know that Kinyua spent 1/4 of his net January salary on school fees. Given the total January salary is sh.9450, we can calculate the money spent:
Money spent on school fees = sh.9450 × 1/4 = sh.2362.50
Therefore, Kinyua spent sh.2362.50 on school fees.
c) To find the money spent on transport, we know that Kinyua spent 1/9 of what remained after school fees on transport. Let's calculate the remaining amount after school fees:
Remaining amount after school fees = sh.9450 - sh.2362.50 = sh.7087.50
Now, we can calculate the money spent on transport:
Money spent on transport = sh.7087.50 × 1/9 = sh.787.50
Therefore, Kinyua spent sh.787.50 on transport.
d) Finally, to find the money spent on electricity and water bills, we need to subtract the amount spent on school fees and transport from the total January salary:
Money spent on electricity and water bills = Total January salary - Money spent on school fees - Money spent on transport
= sh.9450 - sh.2362.50 - sh.787.50
= sh.6300
Therefore, Kinyua spent sh.6300 on electricity and water bills.