Mukasa spends 1/4 of her salary on food, 2/5 of the remainder on rent and saves shs.54000. How much is her salary?
her salary --- x
after food she has left 3/4 x
spends 2/5 of that on rent leaving her with (3/5)(3x/4) = (9/20)x
9x/20 = 54000
x = 120000
check
spent on food: (1/4) of 120000 = 30000
leaving her with 90000
spends 2/5 of 90000 or 36000 on rent, leaving
her with 90000-36000 = 54000 for savings
Let's assume Mukasa's salary is represented by the variable "x".
Mukasa spends 1/4 of her salary on food, which is (1/4) * x.
The remainder of her salary after spending on food is x - (1/4) * x.
Mukasa then spends 2/5 of the remainder on rent, which is (2/5) * (x - (1/4) * x).
After spending on food and rent, Mukasa saves shs.54000. Therefore, we have the equation:
(2/5) * (x - (1/4) * x) = 54000.
To find x, let's solve the equation step-by-step:
(2/5) * (x - (1/4) * x) = 54000
Multiplying both sides of the equation by 5/2:
x - (1/4) * x = 54000 * (5/2)
Simplifying the right side of the equation:
x - (1/4) * x = 135000
Combining like terms on the left side of the equation:
(3/4) * x = 135000
Dividing both sides of the equation by 3/4:
x = 135000 / (3/4)
Simplifying the right side of the equation:
x = 135000 * (4/3)
Calculating the value of x:
x = 180000
Therefore, Mukasa's salary is shs.180000.
To find Mukasa's salary, we need to work backwards from the amount she saves.
Let's assume her salary is x.
First, she spends 1/4 of her salary on food, so she has 3/4 of her salary remaining. This can be represented as (3/4)x.
Next, she spends 2/5 of the remaining amount on rent, leaving her with 3/5 of the remaining amount. This can be represented as (3/5)*(3/4)x.
Finally, we know that she saves shs.54000, so we can set up the equation: (3/5)*(3/4)x = 54000.
To solve for x, we can simplify the equation.
First, multiply the fractions: (3/5)*(3/4) = 9/20.
So the equation becomes: (9/20)x = 54000.
To isolate x, we can multiply both sides of the equation by the reciprocal of 9/20, which is 20/9.
(20/9)*(9/20)x = (20/9)*54000.
Simplifying, we find: x = 120,000.
Therefore, Mukasa's salary is shs.120,000.