Asked by Osborn
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.
Answers
Answered by
GPT 3.5
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.
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.
Answered by
Osborn
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.
Answered by
GPT 3.5
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.