Math Problem Statement

Guadalupe bought snacks for her team's practice. She bought a bag of chips for $1.93 and a 15-pack of juice bottles. The total cost before tax was $32.83. Write and solve an equation which can be used to determine x, how much each bottle of juice cost.

Solution

To solve this problem, let's define xx as the cost of each bottle of juice.

Step-by-Step Solution:

  1. Guadalupe bought:

    • A bag of chips for $1.93.
    • A 15-pack of juice bottles, each costing xx dollars.
  2. The total cost of the juice bottles is 15x15x.

  3. The total cost of everything was $32.83.

  4. We can set up an equation based on the total cost: 1.93+15x=32.831.93 + 15x = 32.83

  5. To find xx, solve the equation: 15x=32.831.9315x = 32.83 - 1.93 15x=30.9015x = 30.90 x=30.9015x = \frac{30.90}{15} x=2.06x = 2.06

Solution:

  • Equation: 1.93+15x=32.831.93 + 15x = 32.83
  • Answer: x=2.06x = 2.06

Each bottle of juice costs $2.06.

Would you like further details or have any questions?


Here are five related questions you might find interesting:

  1. How would the equation change if the bag of chips cost $2.50 instead of $1.93?
  2. If the total cost after tax was $35.00, how would you modify the equation to include a 7% tax?
  3. What if Guadalupe bought 20 juice bottles instead of 15? How would that affect the cost per bottle?
  4. If Guadalupe had a budget of $30, what is the maximum number of juice bottles she could buy if each bottle costs $2.06?
  5. How would the solution differ if there was a discount on the juice bottles that reduced the total by $5?

Tip: Always double-check your calculations when dealing with multiple costs and variables to avoid simple mistakes!

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations

Formulas

Total cost = cost of chips + (number of bottles * cost per bottle)

Theorems

Basic algebraic manipulation for solving linear equations

Suitable Grade Level

Grades 6-8