Question(7) In January, Mambo donated $1 / 6$ of his salary to a children's home while Simba donated $1 / 5$ the of his salary to the same children's home. Their total donation for January was Ksh 14820.In February, Mambo donated 1/8 of his salary to the children's home while Simba donated $1 / 12$ of his salary to the children's home. Their total donation for February was Ksh 8675 . Calculate Mambos monthly salary.

Studdy Solution
Solve the system of equations to find Mambo's salary.
First, let's eliminate fractions by multiplying each equation by the least common multiple of the denominators.
For the January equation, multiply by 30: $$5M + 6S = 444600$$
For the February equation, multiply by 24: $$3M + 2S = 208200$$
Now, solve the system of equations:
1. $5M + 6S = 444600$
2. $3M + 2S = 208200$
To eliminate $S$, multiply the second equation by 3: $$9M + 6S = 624600$$
Subtract the first equation from this result: $$(9M + 6S) - (5M + 6S) = 624600 - 444600$$ $$4M = 180000$$
Solve for $M$: $$M = \frac{180000}{4}$$ $$M = 45000$$
Mambo's monthly salary is: $$\boxed{45000}$$