A bridge can hold a maximum of 75,000 pounds. A truck that weighs 40,000 pounds carries boxes that weigh 40 pounds each. What is the maximum number of boxes the truck can carry to cross the bridge? Express your answer as an inequality.(1 point)

Question

b≤

Answer 1

To determine the maximum number of boxes \( b \) that the truck can carry while crossing the bridge, we can set up the following inequality:

1. The weight of the truck is 40,000 pounds.
2. Each box weighs 40 pounds.
3. The maximum weight the bridge can hold is 75,000 pounds.

The total weight of the truck plus the boxes can be expressed as:

\[ 40,000 + 40b \]

where \( b \) is the number of boxes. To ensure that the total weight does not exceed the bridge's maximum capacity, we set up the inequality:

\[ 40,000 + 40b \leq 75,000 \]

Now, we can solve for \( b \):

1. Subtract 40,000 from both sides:

\[ 40b \leq 75,000 - 40,000 \]

\[ 40b \leq 35,000 \]

2. Divide both sides by 40:

\[ b \leq \frac{35,000}{40} \]

\[ b \leq 875 \]

Thus, the maximum number of boxes the truck can carry to cross the bridge is represented by the inequality:

\[ b \leq 875 \]

In summary: \[ b \leq 875 \]