chen bought a bag f groceries weighing 15 pounds.His friend,jo,bought a bag of groceries that always 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 solve this problem, we can use algebraic equations. Let's denote the number of items in Chen's grocery bag as "C" and the number of items in Jo's grocery bag as "J".
Given:
1. The weight of Chen's bag is 15 pounds, so let's set up the equation:
C = 15
2. The weight of Jo's bag is also 15 pounds, but it contains one less item and the average weight per item is 1/2 pound more than Chen's. Let's set up two equations to represent this:
J = C - 1 (As Jo's bag contains one less item)
(15 / J) = (15 / C) + 1/2 (The average weight per item for Jo's groceries is 1/2 pound more than for Chen's)
Now, we can substitute the value of C from equation 1 into equations 2:
J = 15 - 1 = 14
(15 / J) = (15 / 15) + 1/2
15 / J = 1 + 1/2
15 / J = 3/2
To solve for J, we can cross-multiply:
15 * 2 = 3 * J
30 = 3J
Finally, we divide both sides of the equation by 3 to find the value of J:
J = 30 / 3 = 10
Therefore, Jo's grocery bag contains 10 items.