When heavy rain ruined the banana crop in Central​ America, the price of bananas rose from ​$0.70 a pound to ​$0.90 a pound.

Question

Growers sold fewer​ bananas, but their total revenue remained unchanged.

What is the change in percent (Answer with whole number)

Answer 1

There is a very simple and logical way to solve this problem. I will first right down the verbal logical way and then show how its done with equations.

Method 1)

We start by picking a number for initial sale of bananas at $0.70. An easy number to work with is 100 pounds. Lets use that and calculate total revenue at $0.70 per pound. We get 0.70 * 100 = $70 in total revenue. Now we know that the total revenue for both scenarios (Bananas sold at $0.70 and bananas sold at $0.90) is the same. So the total pounds of bananas sold at $0.90 must yield a total revenue of $70. $0.90 * x = $70 so to get x we divide $70 by $0.90 and we get 77.78 pounds of Bananas sold.

To get the percent change is pounds of bananas sold we use the equation [(End - Beginning)/Beginning] * 100 So we get [(77.78-100)/100] *100 = -22% rounded down to a whole number.

You can do a check to make sure this is correct by following the logic in the question. Less bananas were sold at $0.90 than at $0.70 (77.78 < 100).

Equation Method:

$0.70 * x = P

P = $0.9 * y

Pick a number for x and solve for P. (x = 100)

$0.70 * 100 = 70 --> 70 = $0.90 * y --> y = 70/0.9 --> y = 77.78

Percent Change here is [(77.78 - 100)/ 100] * 100 = - 22% Rounded down to the nearest whole number.