Five-twelfths of my salary was spend on food, then I gave 3/7 of the remainder to my sister and had 856 pesos left. How much did I spend for food?
5/12 + (3/7)(7/12) = 5/12 + 3/12 = 2/3
So, 1/3 of the original amount = 856
To solve this problem, we need to follow a step-by-step approach.
Let's assume your salary as 'X' pesos.
According to the given information, you spent five-twelfths of your salary on food. So, the amount you spent on food can be calculated as (5/12) * X.
After spending the amount on food, you have the remainder. The remainder can be calculated by subtracting the amount spent on food from your total salary:
Remainder = X - (5/12) * X
Next, you gave 3/7 of the remainder to your sister. Thus, the amount given to your sister can be calculated as (3/7) * Remainder.
Finally, you had 856 pesos left. So, we can set up the equation:
Remainder - (3/7) * Remainder = 856
To find the value of Remainder, we can solve the equation:
(4/7) * Remainder = 856
Now, we can isolate the value of Remainder by dividing both sides of the equation by (4/7):
Remainder = 856 / (4/7)
Simplifying this equation:
Remainder = 856 * (7/4)
Now, substitute the value of Remainder back into the first equation to find the amount spent on food:
Amount spent on food = (5/12) * X
By substituting the value of Remainder, we get:
Amount spent on food = (5/12) * (X - (5/12) * X)
Simplifying this equation:
Amount spent on food = (5/12) * (7/12) * X
Since we know that the amount spent on food is equal to 856 pesos, we can solve for X:
(5/12) * (7/12) * X = 856
By solving this equation, we can find the value of X, which represents your salary.