a man spends 1/9 of his monthly salary on rent,1/2 on food and 1/4 on clothes and other items. if he has GHC 195 left at the end of the month. how much does he earn?
1/9 + 1/2 + 1/4 = 4/36 + 18/36 + 9/36 = 31/36
so
5/36 is left
(5/36 ) x= 195
x = 36 * 195 / 5 = 1404
Let's assume the man's monthly salary is "x" GHC.
According to the given information:
He spends 1/9 of his salary on rent, which is (1/9) * x.
He spends 1/2 of his salary on food, which is (1/2) * x.
He spends 1/4 of his salary on clothes and other items, which is (1/4) * x.
To find the amount he has left at the end of the month, we need to subtract his expenses from his salary:
x - [(1/9) * x + (1/2) * x + (1/4) * x] = 195
Now, we can solve for x:
x -[(1/9) * x + (1/2) * x + (1/4) * x] = 195
Simplifying the equation:
x - (4/36 * x + 18/36 * x + 9/36 * x) = 195
x - (31/36 * x) = 195
5/36 * x = 195
Multiplying both sides by (36/5) to isolate x:
x = (195 * 36) / 5
x = 1404
Therefore, the man earns 1404 GHC per month.
To find out how much the man earns, we can reverse-engineer the problem by calculating the total amount he spends and then subtracting it from the amount he has left.
Let's break down the man's monthly expenses:
1/9 of his salary goes towards rent.
1/2 of his salary goes towards food.
1/4 of his salary goes towards clothes and other items.
We can add these fractions together to find the total fraction of his salary that he spends:
1/9 + 1/2 + 1/4 = 2/18 + 9/18 + 4/18 = 15/18.
Therefore, the man spends 15/18 of his monthly salary on various expenses.
Now, we know that he has GHC 195 left at the end of the month. This remaining amount is equal to 3/18 (since 18/18 - 15/18 = 3/18) of his monthly salary.
To find the value of 3/18 of his monthly salary being GHC 195, we can set up a proportion:
(3/18) / x = GHC 195 / GHC y,
where x represents his monthly salary, and y represents the value of 1.
To solve for x, we can cross-multiply and solve for x:
(3/18) * GHC y = GHC 195,
3y = 18 * 195,
3y = 3510,
y = 1170.
So, y = 1170 represents the value of 1 in GHC.
Now we can substitute y back into the equation:
(3/18) * x = GHC 195.
We can multiply both sides of the equation by 18/3 to solve for x:
x = (195 * 18) / 3,
x = 1170.
Therefore, the man earns GHC 1170 per month.