Question

M6|L17  Modeling with Inequalities

Sign out

Mr. Tanaka is loading his boat with many identical 45-pound boxes. Mr. Tanaka weighs 190 pounds. The boat can carry at most 1,000 pounds. If each box is fully-filled, how many boxes can he load on the boat?

Complete the statement so that it represents the solution to the inequality.

190+45x ≤ 1000

x 

 

≥

>

<

≤

 

190+45x=1000
x=18

Answer 1

To determine how many boxes Mr. Tanaka can load on the boat while considering the total weight limit, we start with the inequality:

\[ 190 + 45x \leq 1000 \]

Here, \( x \) represents the number of boxes Mr. Tanaka is loading.

To find the maximum number of boxes he can load, we need to solve this inequality step-by-step:

1. Subtract 190 from both sides:

\[ 45x \leq 1000 - 190 \]
\[ 45x \leq 810 \]

2. Next, divide both sides by 45:

\[ x \leq \frac{810}{45} \]
\[ x \leq 18 \]

This means Mr. Tanaka can load at most 18 boxes. Therefore, the complete statement representing the solution to the inequality is:

\[ 190 + 45x \leq 1000 \]

with

\[ x \]

as:

\[ \leq \]

So, the completed statement is:

**"The number of boxes \( x \) can be at most 18."**