Question

Complete the explanation of a real-world situation that could be modeled by |x − 13| = 5. There are supposed to be blank biscuits in a frozen package, but there could be as many as blank extra or blank fewer in each bag, depending on the weight of the biscuits. Solving the equality will give the highest and lowest amounts of biscuits in the bag.

Answer 1

The absolute value equation |x − 13| = 5 represents a situation where there are supposed to be 13 biscuits per bag, but variations in weight mean there could be between 8 and 18 biscuits.

Step-by-step explanation:

A real-world situation that could be modeled by the equation |x − 13| = 5 is that there are supposed to be 13 biscuits in a frozen package, but due to variations in biscuit weight, there could be as many as 5 extra or 5 fewer biscuits in each bag. To find out the highest and lowest number of biscuits that can be in a package, we can solve the absolute value equation. Let's solve the equation step-by-step:

1. The absolute value expression |x − 13| equals 5 means that the quantity inside the absolute value (x − 13) is 5 units away from zero on the number line, either in the positive or negative direction.

2. So, we can have two scenarios: either (x − 13) = 5 or (x − 13) = − 5.

3. Solving the first equation (x − 13) = 5, we add 13 to both sides to isolate x, which gives us x = 18. This indicates the maximum number of biscuits could be 18.

4. Solving the second equation (x − 13) = − 5, we also add 13 to both sides to isolate x, which results in x = 8. This shows the minimum number of biscuits that could be in the package is 8.

   Therefore, a package of biscuits could have between 8 and 18 biscuits, depending on their weight.