Question 1124466


in general, total cost is equal to the quantity bought * the price per unit of quantity bought.


when the quantity is 10 kilograms, and the price is x per kilogram, then the total cost is 10 * x.


if the price goes up 32%, then the total cost becomes 10 * 1.32 * x = 13.2 * x.


but the family wants the total cost to be only 10% higher.


in other words, they want the total cost to be equal to 11 * x.


the new price per kilogram will still be 1.32.


the quantity, however, can be reduced so the total cost is 1.10 * x.


let y = the new quantity.


you get y * 1.32 * x = 11 * x.


divide both sides of this equation by 1.32 * x to get:


y = (11 * x) / (1.32 * x)


simplify to get y = 11 / 1.32 = 8.33333..... = 8 and 1/3 kilograms.


if they reduce the quantity from 10 kilograms to 8 and 1/3 kilograms, then the overall cost will only be 10% higher rather than 32% higher.


8 and 1/3 * 1.32 * x = 11 * x.


the total cost went up from 10 * x to 11 * x.


that's a 10% increase in total cost.


as an example, assume the original price per kilogram was 5 dollars.


the family buys 10 kilogram * 5 dollars per kilogram = 50 dollars.


the price goes up 32% so the price is now 6.6 dollars per kilogram.


the family reduces their consumption to 8 and 1/3 kilograms.,


the new total cost is 8 and 1/3 * 6.6 = 55 dollars.


that's a 10% increase in total cost because (55 - 50) / 50 = 5 / 10 = .1 = 10%.