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Enter the correct answer in the box. Write your answer in the form [tex]\(at + bm \leq c\)[/tex].

Denise needs to move some bags of gardening soil from her garage to her mother's garden. The topsoil weighs 30 pounds per bag, and the mulch weighs 30 pounds per bag. The wagon she is using carries a maximum of 330 pounds.

The table shows the first three loads of topsoil and mulch she has carried in the wagon.

[tex]\[
\begin{tabular}{|c|c|c|c|}
\hline
\begin{tabular}{c}
Topsoil, $t$ \\ (bags)
\end{tabular}
& 7 & 2 & 3 \\
\hline
\begin{tabular}{c}
Mulch, $m$ \\ (bags)
\end{tabular}
& 3 & 6 & 8 \\
\hline
\end{tabular}
\][/tex]

Write a linear inequality to describe the bags of topsoil and mulch the wagon can carry at one time.



Answer :

GinnyAnswer
To write a linear inequality that describes the number of bags of topsoil and mulch the wagon can carry at one time, follow these steps:

1. Identify Variables:
- Let [tex]\( t \)[/tex] represent the number of topsoil bags.
- Let [tex]\( m \)[/tex] represent the number of mulch bags.

2. Determine Weights:
- Each bag of topsoil weighs 30 pounds.
- Each bag of mulch weighs 30 pounds.

3. Maximum Weight Capacity:
- The wagon can carry a maximum of 330 pounds.

4. Formulate the Equation:
- The sum of the weights of the topsoil bags and the mulch bags must not exceed 330 pounds.
- This can be written as: [tex]\( 30t + 30m \leq 330 \)[/tex]

5. Simplify the Inequality:
- To simplify, divide each term by 30:
[tex]\[ t + m \leq 11 \][/tex]

Therefore, the linear inequality describing the relationship between the number of bags of topsoil [tex]\( t \)[/tex] and mulch [tex]\( m \)[/tex] that the wagon can carry at one time is:

[tex]\[ 30t + 30m = 330 \][/tex]

However, if you need it in inequality form to allow for potentially underfilling the wagon, it should be:

[tex]\[ 30t + 30m \leq 330 \][/tex]

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