Sarah bought snacks for her team’s practice. She bought a bag of chips for $1.56 and a 20-pack of juice bottles. The total cost before tax was $33.96. Write and solve an equation which can be used to determine j, how much each bottle of juice cost.
The correct answer and explanation is:
To determine how much each bottle of juice cost, we can set up an equation based on the information given.
Step 1: Identify the components in the problem.
- Sarah bought a bag of chips for $1.56.
- Sarah bought a 20-pack of juice bottles, and we are asked to find the cost of each bottle of juice (denoted as j).
- The total cost before tax is $33.96.
Step 2: Set up the equation.
The total cost of the snacks consists of the cost of the bag of chips plus the cost of the 20 bottles of juice. The cost of the juice is 20 times the cost per bottle, which is j. The equation will look like this: 1.56+20j=33.961.56 + 20j = 33.96
Step 3: Solve for j.
To solve for j, subtract the cost of the chips ($1.56) from both sides of the equation: 20j=33.96−1.5620j = 33.96 – 1.56 20j=32.4020j = 32.40
Next, divide both sides of the equation by 20 to isolate j: j=32.4020j = \frac{32.40}{20} j=1.62j = 1.62
Step 4: Interpret the result.
The cost of each bottle of juice is $1.62.
Explanation:
The problem asks us to find the price per juice bottle by using the total cost of all the snacks. By breaking down the total cost into the sum of the price of the chips and the cost of the juice bottles, we created an equation. We then solved the equation step by step to find that the cost of each bottle of juice is $1.62. This approach is a straightforward application of algebra to solve for an unknown in a real-world context.