Math  /  Algebra

Question(7) In January, Mambo donated 1/61 / 6 of his salary to a children's home while Simba donated 1/51 / 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 1/121 / 12 of his salary to the children's home. Their total donation for February was Ksh 8675 . Calculate Mambos monthly salary.

Studdy Solution

STEP 1

1. Let M M represent Mambo's monthly salary.
2. Let S S represent Simba's monthly salary.
3. In January, Mambo donated 16 \frac{1}{6} of his salary.
4. In January, Simba donated 15 \frac{1}{5} of his salary.
5. Their total donation in January was Ksh 14820.
6. In February, Mambo donated 18 \frac{1}{8} of his salary.
7. In February, Simba donated 112 \frac{1}{12} of his salary.
8. Their total donation in February was Ksh 8675.
9. We need to calculate Mambo's monthly salary.

STEP 2

1. Set up equations based on the January donations.
2. Set up equations based on the February donations.
3. Solve the system of equations to find Mambo's salary.

STEP 3

Set up equations based on the January donations.
For Mambo, the donation is 16M \frac{1}{6}M . For Simba, the donation is 15S \frac{1}{5}S .
The equation for January is: 16M+15S=14820 \frac{1}{6}M + \frac{1}{5}S = 14820

STEP 4

Set up equations based on the February donations.
For Mambo, the donation is 18M \frac{1}{8}M . For Simba, the donation is 112S \frac{1}{12}S .
The equation for February is: 18M+112S=8675 \frac{1}{8}M + \frac{1}{12}S = 8675

STEP 5

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 5M + 6S = 444600
For the February equation, multiply by 24: 3M+2S=208200 3M + 2S = 208200
Now, solve the system of equations:
1. 5M+6S=444600 5M + 6S = 444600
2. 3M+2S=208200 3M + 2S = 208200

To eliminate S S , multiply the second equation by 3: 9M+6S=624600 9M + 6S = 624600
Subtract the first equation from this result: (9M+6S)(5M+6S)=624600444600 (9M + 6S) - (5M + 6S) = 624600 - 444600 4M=180000 4M = 180000
Solve for M M : M=1800004 M = \frac{180000}{4} M=45000 M = 45000
Mambo's monthly salary is: 45000 \boxed{45000}

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