at a store you bought 2 pounds of apples and 1 1/3 pounds of grapes. If the store's scale measures to the nearest half pound, what is the range of possible actual weights for the sum of both purchases of fruits.
I would not see a range. Since the 1 1/3 (1.33) pound is more than half way to 1 1/2 (1.50), I would assume that it registers 3.5. However, if you need a range, I would say 3.0-3.5.
To determine the range of possible actual weights for the sum of both purchases of fruits, we need to consider the possible weights for each item within the measurement precision of the store's scale.
Let's start with the apples. You bought 2 pounds of apples. Since the store's scale measures to the nearest half pound, the actual weight of the apples can be anywhere between 1.75 pounds (2 pounds rounded down) to 2.25 pounds (2 pounds rounded up).
Next, let's consider the grapes. You bought 1 1/3 pounds of grapes, which is equivalent to 4/3 pounds. Similar to the apples, the actual weight of the grapes can be between 1.25 pounds (4/3 pounds rounded down) and 1.75 pounds (4/3 pounds rounded up).
Now, let's calculate the range of possible weights for the sum of both purchases. We'll add the lowest possible weights and the highest possible weights of the apples and grapes:
Lowest possible weight: 1.75 pounds (apples) + 1.25 pounds (grapes) = 3 pounds
Highest possible weight: 2.25 pounds (apples) + 1.75 pounds (grapes) = 4 pounds
Therefore, the range of possible actual weights for the sum of both purchases of fruits is between 3 pounds and 4 pounds.