All spent half of his June salary on school fees, 1/4 on farming, and 2/5 of the remainder on food. Calculate his June salary if he spent Sh 3200 on food?
Answer (1)
Let's solve the problem step-by-step to find out All's June salary.
Understand the problem:
All spends half ( 2 1 ) of his June salary on school fees.
He spends 4 1 of the total salary on farming.
The remaining part of the salary is then used and he spends 5 2 of this remainder on food.
We're given that he spent Sh 3200 on food.
Let All's June salary be x .
Calculate remaining salary after school fees and farming:
After spending half on school fees, the balance is:
x − 2 1 x = 2 1 x
From this remaining half, another [tex]\frac{1}{4}[/tex] of the total salary [tex]x[/tex] is spent on farming:
2 1 x − 4 1 x = 4 1 x
So, the remaining amount before spending on food is [tex]\frac{1}{4}x[/tex].
Calculate the amount spent on food:
It is given that he spends 5 2 of the remainder on food, and this equals Sh 3200 .
5 2 × 4 1 x = 3200
Solve for x :
Simplify and solve for x :
5 2 × 4 1 x = 3200 20 2 x = 3200 10 1 x = 3200
Multiply both sides by 10 to solve for [tex]x[/tex]:
x = 3200 × 10 = 32000
Conclusion:
All's June salary is Sh 32000 .
