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]
