Chen bought a bag of groceries weighing 15 pounds, His friend, Jo, bought a bag of groceries that also weighed 15 pounds, but contained one less item. The average weight per item for Jo's groceries was 1/2 pound more than for Chen's. How many items were in Jo's grocery bag?
To find the number of items in Jo's grocery bag, we can first determine the average weight per item for Chen's groceries. Let's call the number of items in Chen's bag "n".
The total weight of Chen's groceries is 15 pounds, so the weight per item is 15/n pounds.
Next, we can determine the average weight per item for Jo's groceries. Since Jo's groceries weigh the same (15 pounds) but contain one less item, let's call the number of items in Jo's bag "n-1".
The weight per item for Jo's groceries is (15 pounds)/(n-1) pounds.
According to the given problem, the average weight per item for Jo's groceries is 1/2 pound more than for Chen's. Therefore, we can set up the following equation:
(15 pounds)/(n-1) = (15 pounds)/(n) + 1/2
To simplify the equation, we can multiply both sides by 2n(n-1) to eliminate the denominators:
2(15) = 2(15)(n) + (n-1)(2n)
30 = 30n + 2n^2 - 2n
30 = 2n^2 + 28n
2n^2 + 28n - 30 = 0
To solve this quadratic equation, we can apply the quadratic formula:
n = (-b ± √(b^2 - 4ac)) / 2a
Here, a = 2, b = 28, and c = -30.
Using the quadratic formula, we find two possible values for n: n ≈ -28.13 and n ≈ 0.13.
Since the number of items cannot be negative or a decimal, we can consider n ≈ 0.13 as not possible in this context. Therefore, we disregard this solution.
Thus, the number of items in Jo's grocery bag is approximately 28.