Question

A student spends two three-week summer sessions in London. She only consumes food and tube rides. During the first session, she spends 50 pounds on 10 underground rides, and 300 pounds on 100 units of food.

Before the second session, fares increase 10% but the price of food remains fixed.

Suppose she spends 49.5 pounds on the underground in the second session. What expenditures on food would show she is better or worse off?

Answer 1

Here the student spend initially 50 pounds on 10 underground rides. So price or cost of each underground rides is 50/10 = 5 pounds. The student spends 300 pounds on 100 units of food. So price of per unit of food is 300/100 = 3 pound. Therefore we can say 1 underground ride = 5/3 =1.666 foods. If we take 1 less of underground food there need to take 1.666 more food to compensate that.

Initial price of ride was 5 pounds and if it is increases by 10% then new price will be 5.50 pounds. The student spend 49.5 pounds on underground rides in second season i.e after price or cost ride rise. New level of underground rides will be 49.5/5.5 =9 rides. Initially the student took 10 rides in first session. Here the student is taking 1 less ride. So to compensate this there need to take more food. In New condition price of ride is 5.5 and price of food is 3 and therefore 1 ride is equivalent to 5.5/3 = 1.8333 foods. So to compensate this there need to take 1.8333 foods. The cost cost of 1.8333 food will be 1.8333*3 = 5.5 pounds. Therefore we can say if the student spends anything less than 305.5 pounds (300+5.5 = 305.5) on food the student will be worse off. If the student spends more than 305.5 pounds on food then the student will be better off. So we can summarise as follows- Spend on food less than 305.5 pounds implies worse off. Spend on food equal to 305.5 pounds is neither worse off nor better off. Spending more than 305.5 will be better off situation.