SOLUTION: Price of sugar is increased by 25%. The percentage of consumption to be decreased so that there would be no increase in the expenditure??

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: Price of sugar is increased by 25%. The percentage of consumption to be decreased so that there would be no increase in the expenditure??      Log On


   



Question 1122371: Price of sugar is increased by 25%. The percentage of consumption to be decreased so that there would be no increase in the expenditure??
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
p is the current price of sugar.
q is the current quantity of sugar.

the total cost is equal to p * q.

when the price of sugar is increased by 25%, the price becomes 1.25 * p.

to keep the total cost the same, you will need to divide the quantity by 1.25.

you will get total cost is equal to 1.25 * p * q / 1.25 which becomes total cost is equal to p * q.

q / 1.25 is equal to 1/1.25 * q which is equal to .8 * q.

.8 * q is equal to q - .2 * q.

therefore, if the price goes up 25%, the quantity needs to come down 20% so that the total cost remains the same.

for example:

assume the price is 100 and the quantity is 100.

the total cost if 100 * 100 = 10,000.

when the price goes up 25%, the price becomes 125.

when the quantity comes down 20%, the quantity becomes 80.

125 * 80 = 10,000.

the total cost remains the same.