Question

enter the correct answer in the box. write your answer in the form \\(at + bm \le c\\).

denise needs to move some bags of gardening soil from her garage to her mothers 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.

\

$$\begin{tabular}{|c|c|c|c|} \\hline topsoil, \\(t\\) (bags) & 7 & 2 & 3 \\\\ \\hline mulch, \\(m\\) (bags) & 3 & 6 & 8 \\\\ \\hline \\end{tabular}$$

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

Explanation:

Identify variables and weights

The variables are defined as:

• \(t\): number of bags of topsoil
• \(m\): number of bags of mulch

The weights per bag are:

• Topsoil: \(30\) pounds per bag
• Mulch: \(30\) pounds per bag

Determine total weight expression

Using the Linear Inequalities concept, the total weight of \(t\) bags of topsoil and \(m\) bags of mulch is:

$$ 30t + 30m $$

Set up the inequality

The wagon carries a maximum of \(330\) pounds.
"Maximum" means the total weight must be less than or equal to \(330\):

$$ 30t + 30m \le 330 $$

Format the final inequality

The prompt asks to write the answer in the form \(at + bm \le c\) (or similar inequality sign).
Thus, the inequality is:

$$ 30t + 30m \le 330 $$

Answer:

Write a linear inequality to describe the bags of topsoil and mulch the wagon can carry at one time. <blank>\(30t + 30m \le 330\)</blank>