Let's start by finding out how much money Kofi had left after spending 2/11 of his salary on food.
If the amount he had left after spending 2/11 on food is represented by x, then the equation becomes x*(1 - 2/11) = x*(9/11) = 9x/11.
He then spent 3/8 of the remaining amount on rent, so the equation becomes (9x/11)*(1 - 3/8) = (9x/11)*(5/8) = 45x/88.
Finally, he spent 1/4 of the remaining amount on books, so the equation becomes (45x/88)*(1 - 1/4) = (45x/88)*(3/4) = 135x/352.
After all these expenses, he had 200 cedis left, so the equation becomes 135x/352 - 200 = 0.
To find x, we can multiply both sides of the equation by 352: 135x - 200*352 = 0.
Which can be simplified to 135x - 70400 = 0.
Adding 70400 to both sides of the equation: 135x = 70400.
Dividing both sides of the equation by 135: x = 70400/135 = 521.481.
Therefore, Kofi's monthly salary is approximately 521.481 Ghana cedis.
Kofi spent 2/11 of his monthly salary on food , 3/8 of the remainder on rent and 1/4 of what still remained on books. If he still has 200 Ghana cedis left. What is Kofi's salary per month.
3 answers
Kofi spent 2/11 of his monthly salary on food , 3/8 of the remainder on rent and 1/4 of what still remains on books. If he still has 200 Ghana cedis left. What is Kofi's salary per month.
Let's represent Kofi's monthly salary as 'S'.
Kofi spent 2/11 of his salary on food, so the amount spent on food is (2/11) * S = (2S)/11.
The remainder after spending on food is (S - (2S)/11) = (9S)/11.
Kofi spent 3/8 of the remainder on rent, so the amount spent on rent is (3/8) * (9S)/11 = (27S)/88.
The amount that remains after spending on rent is ((9S)/11 - (27S)/88).
Kofi spent 1/4 of what still remains on books, so the amount spent on books is (1/4) * ((9S)/11 - (27S)/88) = (9S)/44 - (27S)/352 = (99S - 27S)/352 = (72S)/352.
The amount that remains after spending on books is ((9S)/11 - (27S)/88) - (72S)/352 = (72S - 27S - 72S)/352 = (-27S)/352.
Given that Kofi has 200 Ghana cedis left, we can equate the remaining amount to 200:
(-27S)/352 = 200.
Multiplying both sides of the equation by 352:
-27S = 200 * 352.
-27S = 70400.
Dividing both sides of the equation by -27:
S = -70400 / 27.
Therefore, Kofi's monthly salary is approximately -2607.41 Ghana cedis.
Kofi spent 2/11 of his salary on food, so the amount spent on food is (2/11) * S = (2S)/11.
The remainder after spending on food is (S - (2S)/11) = (9S)/11.
Kofi spent 3/8 of the remainder on rent, so the amount spent on rent is (3/8) * (9S)/11 = (27S)/88.
The amount that remains after spending on rent is ((9S)/11 - (27S)/88).
Kofi spent 1/4 of what still remains on books, so the amount spent on books is (1/4) * ((9S)/11 - (27S)/88) = (9S)/44 - (27S)/352 = (99S - 27S)/352 = (72S)/352.
The amount that remains after spending on books is ((9S)/11 - (27S)/88) - (72S)/352 = (72S - 27S - 72S)/352 = (-27S)/352.
Given that Kofi has 200 Ghana cedis left, we can equate the remaining amount to 200:
(-27S)/352 = 200.
Multiplying both sides of the equation by 352:
-27S = 200 * 352.
-27S = 70400.
Dividing both sides of the equation by -27:
S = -70400 / 27.
Therefore, Kofi's monthly salary is approximately -2607.41 Ghana cedis.
1 answer