Let us consider various steps of mathematical modeling and solve this problem.
Step 1. Formulation of the problem : Price of sugar goes up by 40% i.e. if the family spends Rs. 100 on sugar, then with the increase in price, the family will have to spend Rs. 140. But the family decides not to increase the expenditure, instead it prefers to reduce the consumption of sugar.
Mathematical formulation :
Suppose the family consumed × kg of sugar for Rs. 100 before the price hike.
∴ the increased prince of x k of sugar is Rs. 140.
Quantity of sugar that can be bought for Rs. 100 at the increased price
= x/140 x 100 = 10x/14kg
∴ reduction in quantity of sugar
= x - 10x/14 = 4x/147kg
Step 2. Finding the solution : Percent reduction in consumption of sugar
Step 3. Interpretation of the solution :
The family should reduce the consumption of sugar by 28(4/7)%
Step 4. Validation of result :
After increase in price of sugar, the amount of sugar bought by the family.
