Final answer:
To determine which barrel was left out, calculate the value of each barrel based on the price per gallon. The barrel with the lowest value was left out.
Step-by-step explanation:
To determine which barrel was left out, we need to analyze the problem. The oil sells for twice as much per gallon as the vinegar. The customer buys $14 worth of each. So, let's assume the vinegar sells for $x per gallon. Since the customer buys $14 worth of vinegar, we can write the equation: $x * (5 barrels) = $14. Solving for x, we find that x = $2.80. Therefore, the oil sells for twice as much, which is $2.80 * 2 = $5.60 per gallon.
To find out which barrel was left, we need to calculate the total value of each barrel. The total value is calculated by multiplying the number of gallons in each barrel by the price per gallon. For example, the barrel with 15 gallons of vinegar is worth 15 * $2.80 = $42. The barrel with 8 gallons of oil is worth 8 * $5.60 = $44. Continuing this calculation for each barrel, we find that the barrel with 15 gallons of vinegar was left because it has the lowest value.