Mathematics

Full Answer Section

. Least Possible Number:

• The least common multiple (LCM) of 30, 45, and 54 is 540.
• Adding the remainder of 29, the least possible number is 540 + 29 = 569.

4. Maximum Books per Group:

• The greatest common divisor (GCD) of 36, 32, and 28 is 4.
• The maximum number of books per group is 4.

5. Ratio m:n:

• Cross-multiplying the given ratio, we get 5(5m - 2n) = 7(2m - n).
• Expanding and simplifying, we get 25m - 10n = 14m - 7n.
• Combining like terms, we get 11m = 3n.
• Therefore, the ratio m:n is 3:11.

7. Mother's Age in 15 Years:

• Let's use d for the daughter's current age and m for the mother's current age.
• We're given m = 3.5d and (m-5) + (d-5) = (m+4).
• Simplifying the second equation, we get d = 14.
• Substituting d in the first equation, we get m = 49.
• The mother's age in 15 years will be 49 + 15 = 64 years.

8. Forex Bureau:

a) Amount in Kenya shillings = 20,730 Euros * 144.60 Ksh/Euro = 3,001,458 Ksh.

b) Amount remaining after spending = 3,001,458 Ksh - 2,410,300 Ksh = 591,158 Ksh. Amount in US Dollars = 591,158 Ksh / 133.40 Ksh/USD ≈ 4,431 USD (rounded to nearest dollar).

I'm ready to complete questions 1, 6, and 9 as soon as you provide the necessary information.

Sample Solution

2. Oilibya Filling Station Profit:

• Let's represent the amount of petrol sold as P and diesel as D.
• We know D = 2P and P + D = 900,000 liters.
• Substituting D, we get P + 2P = 900,000, which gives P = 300,000 liters and D = 600,000 liters.
• Profit from petrol = 300,000 liters * 520 Ksh/1000 liters = 156,000 Ksh.
• Profit from diesel = 600,000 liters * 480 Ksh/1000 liters = 288,000 Ksh.
• Total profit = 156,000 Ksh + 288,000 Ksh = 444,000 Ksh.