SOLUTION: The 31st of December 1994, a TV costs 80,000 pesos. The 31st of December 1995, its price was 50% higher than the previous year. The 31st of December 1996, its price was 33% highe

Question 1098482: The 31st of December 1994, a TV costs 80,000 pesos. The 31st of December
1995, its price was 50% higher than the previous year. The 31st of December
1996, its price was 33% higher than the previous year. By approximately what
% must the price decrease to return to the initial price?

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
80,000 * 1.5 = 120,000 * 1.33 = 159,600.

50% of 80,000 is equal to .5 * 80,000 = 40,000.
add that to 80,000 and you get 120,000.

33% of 120,000 is equal to 39,600.
add that to 120,000 and you get 159,600.

80,000 + 50% of 80,000 is equal to 80,000 + .5 * 80,000.

factor out the 80,000 and this becomes 80,000 * (1 + .5) which is then equal to 80,000 * 1.5 which is equal to 120,000.

120,000 + 33% of 120,000 is equal to 120,000 + .33 * 120,000.

factor out the 120,000 and this becomes 120,000 * (1 + .33) which is then equal to 120,000 * 1.33 which is equal to 159,600.

that's how we got from 80,000 to 159,600.

80,000 * 1.5 * 1.33 is the same as multiplying 80,000 * 1.5 and then multiplying the result of that by 1.33.

-----

the original value is 80,000.

the final value is 159,600.

the difference between the two is the increase from the original value to the final value.

the difference between the two is also the decrease from the final value to the original value.

the rate of increase is the increase divided by the original value.

the rate of decrease is the decrease divided by the final value.

the rate of increase is equal to 79,600 / 80,000 = .995 = 99.5%.

the rate of decrease is equal to 79,600 / 159,600 = .4987468672 = 49.87% rounded to two decimal places.

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