Question

a bag of chips costs $2.50 and a bottle of soda costs $1.50. the number of bags of chips you buy and the number of bottles of sodas must be less than or equal to $20.00. write an inequality to represent this problem.

1.50s+2.50c < 20.00
1.50c+2.50s \le 20.00
1.50s+2.50c \le 20.00
1.50c+2.50s > 20.00

Explanation:

Define variables for the items

Let \(c\) represent the number of bags of chips purchased.
Let \(s\) represent the number of bottles of soda purchased.

Determine the cost expression

Each bag of chips costs \(\$2.50\), so the total cost for chips is \(2.50c\).
Each bottle of soda costs \(\$1.50\), so the total cost for sodas is \(1.50s\).
The combined total cost is represented by the expression:

$$1.50s + 2.50c$$

Formulate the inequality

The problem states that the total cost must be "less than or equal to \(\$20.00\)".
The mathematical symbol for "less than or equal to" is \(\le\).
Therefore, we set up the inequality:

$$1.50s + 2.50c \le 20.00$$

Match with the options

We compare our formulated inequality with the given choices:

• \(1.50s + 2.50c < 20.00\) (Incorrect inequality symbol)
• \(1.50c + 2.50s \le 20.00\) (Incorrectly swaps the unit prices for chips and sodas)
• \(1.50s + 2.50c \le 20.00\) (Correct)
• \(1.50c + 2.50s > 20.00\) (Incorrect symbol and swapped prices)

Answer:

• (A) \(1.50s+2.50c < 20.00\)
• (B) \(1.50c+2.50s \le 20.00\)
• (C) \(1.50s+2.50c \le 20.00\) (Correct answer)
• (D) \(1.50c+2.50s > 20.00\)