Question

Max, the owner of a landscaping company, is ordering rakes and shovels from an equipment wholesaler. He doesn't want to spend more than $400 total for his purchases. He can get the rakes at a cost of $14 apiece and the shovels at a cost of $16 apiece.
Write the inequality in standard form that describes this situation. Use the given numbers and the following variables.
x = the number of rakes ordered
y = the number of shovels ordered

Answer 1

To write the inequality that describes Max's purchasing situation, we start with the costs of rakes and shovels as follows:

- Each rake costs $14.
- Each shovel costs $16.
- Max wants to spend no more than $400.

Let \( x \) represent the number of rakes ordered and \( y \) represent the number of shovels ordered. The total cost for the rakes and shovels can be expressed as:

\[
14x + 16y
\]

Since Max does not want to spend more than $400, we can write the inequality:

\[
14x + 16y \leq 400
\]

To put this inequality in standard form, we can rearrange it to align with the form \( Ax + By \leq C \):

\[
14x + 16y \leq 400
\]

This is the standard form of the inequality that describes the situation for Max's purchases of rakes and shovels.