Final answer:
To determine the original amount of money in the student's wallet, we set x as the total money before the purchase. We use the provided information stating that 80% of the money was spent to create the equation 0.80x = money spent, and then solve for x by dividing the spent amount by 0.80.
Step-by-step explanation:
To find out how much money was in the student's wallet before making a purchase at the farmer's market, we need to set up an equation based on the information given. We know that the student spent 80% of their money on 4 pounds of tomatoes and 2 pounds of sweet potatoes. If we let x represent the total amount of money in the student's wallet before the transaction, then 0.80x represents the amount spent at the market.
To construct the equation, since we do not know the individual prices of the tomatoes and sweet potatoes, we cannot calculate the cost directly. Instead, we use the information provided about spending 80% of the wallet's contents, which gives us the equation:
0.80x = money spent at the farmer's market
To solve for x, we would divide the amount spent by 0.80:
x = money spent / 0.80
Once we determine the actual amount spent at the market, we can fill in this value and solve for x to find out how much money was originally in the wallet.