Question

example 11: gene is mailing a package of books to his brother. the post office charges by the weight of the package: a flat fee of $5.90 plus $0.70 per pound. gene also wants to insure the package, which costs $3.50. gene has $13 to spend on shipping. write an inequality describing the number of points gene’s package can weigh.

Explanation:

Step1: Define the variable

Let \( x \) be the weight of the package in pounds.

Step2: Calculate total cost

The cost for shipping is the flat fee plus the cost per pound times weight plus insurance cost. So total cost \( C = 5.90 + 0.70x + 3.50 \).

Step3: Set up the inequality

Since Gene has $13 to spend, the total cost must be less than or equal to $13. So \( 5.90 + 0.70x + 3.50 \leq 13 \).

Step4: Simplify the left side

Combine like terms: \( 9.40 + 0.70x \leq 13 \).

Step5: Solve for x (optional for writing inequality, but to form the inequality as is, we can present the simplified or original. Here the inequality is \( 5.90 + 0.70x + 3.50 \leq 13 \) or simplified \( 0.70x + 9.40 \leq 13 \))

Answer:

The inequality is \( 5.90 + 0.70x + 3.50 \leq 13 \) (or simplified as \( 0.70x + 9.40 \leq 13 \))