at a local grocery store, the bananas they receive are transported through three stages: from the farmer to the market, from the market to the wholesaler, and from the wholesaler to the grocery store. at each stage, the price of the bananas increases by 20% of the previous price. If a person buys 80 cents worth of bananas at the grocery store, how much was the farmer paid for those same bananas?

Question

at a local grocery store, the bananas they receive are transported through three stages: from the farmer to the market, from the market to the wholesaler, and from the wholesaler to the grocery store. at each stage, the price of the bananas increases by 20% of the previous price. If a person buys 80 cents worth of bananas at the grocery store, how much was the farmer paid for those same bananas?

Answer 1

solve for x, the original price of the bananas

x(1.2)^3 = 80

Answer 2

To find out how much the farmer was paid for the bananas, we need to work backwards through the three stages. We'll start with the price at the grocery store and work our way back to the farmer's payment.

Let's assume the price at the grocery store is represented by "x" dollars. According to the given information, at each stage, the price increases by 20% of the previous price. So, let's calculate the previous prices at each stage:

1. Wholesaler's price: If the grocery store sells the bananas for "x" dollars, then the price at the wholesaler would be 20% less than "x" dollars. We can calculate this by multiplying "x" by (100% - 20%):
Wholesaler's price = x - (0.2 * x) = 0.8 * x

2. Market's price: If the wholesaler sells the bananas for 0.8 * "x" dollars, then the price at the market would be 20% less than 0.8 * "x" dollars:
Market's price = 0.8 * x - (0.2 * 0.8 * x) = 0.8 * (0.8 * x) = 0.64 * x

3. Farmer's payment: If the market sells the bananas for 0.64 * "x" dollars, then the farmer's payment would be 20% less than 0.64 * "x" dollars:
Farmer's payment = 0.64 * x - (0.2 * 0.64 * x) = 0.64 * (1 - 0.2) * x = 0.64 * 0.8 * x = 0.512 * x

Now, we know that the person bought the bananas for 80 cents. We need to find the value of "x" that corresponds to 80 cents. Since 1 dollar is equal to 100 cents, we can set up the following equation:

0.512 * x = 80

To solve for "x", divide both sides of the equation by 0.512:

x = 80 / 0.512

Calculating this division, we get:

x = 156.25

So, the price at the grocery store ("x") would be equal to $156.25. Therefore, the farmer would have been paid $156.25 for those same bananas.

solve for x, the original price of the bananas

Jwj,s

To find out how much the farmer was paid for the bananas, we need to work backwards through the three stages. We'll start with the price at the grocery store and work our way back to the farmer's payment.