For a community picnic, Charlie is buying punch priced at $2 per bottle and juice priced at $3 per bottle. He wants to spend no more than $36 on these drinks in total.

Question

Write the inequality in standard form that describes this situation. Use the given numbers and the following variables.
x = the number of bottles of punch
y = the number of bottles of juice

Answer 1

To describe the situation with an inequality in standard form, we can start by defining the costs of the drinks and how they relate to the budget.

Charlie's punch costs $2 per bottle, so the cost for \(x\) bottles of punch is \(2x\). Juice costs $3 per bottle, so the cost for \(y\) bottles of juice is \(3y\). Charlie wants to spend no more than $36 in total on the drinks.

We can express this situation with the following inequality:

\[ 2x + 3y \leq 36 \]

This inequality indicates that the total cost of the punch and juice should not exceed $36.

In standard form, the inequality can be written as:

\[ 2x + 3y - 36 \leq 0 \]

This is the inequality in standard form that describes Charlie's budget for drinks at the picnic.