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Chapter 3: Problem 2

a. Another way to write an equation expressing your change in weight during the first 2 weeks of your diet is to subtract the initial weight, \(154,\) from your final weight, \(149 .\) Then the equation is \(x=149-154,\) where \(x\) represents the change in weight. Determine the value of \(x .\) b. Write a formula to calculate the amount a quantity changes when you know the final value and the initial value. Use the words final value, initial value, and change in quantity to represent the variables in the formula. (Hint: Use the equation from part a as a guide.)

Short Answer

Expert verified
Question: Calculate the change in weight during the first two weeks of the diet and provide a general formula for finding the change in quantity. Answer: The change in weight during the first two weeks of the diet is -5 pounds, which indicates a 5-pound decrease in weight. The general formula for finding the change in quantity is \(C = F - I\), where \(C\) represents the change in quantity, \(F\) is the final value, and \(I\) is the initial value.

Step by step solution

01

Calculate x value

To calculate x, which represents the change in weight during the first two weeks of the diet, we need to subtract the initial weight (154) from the final weight (149) using the given equation: \(x= 149 - 154\).
02

Solving for x

Now, we can find the value of x by performing the subtraction: \(x = 149 - 154 = -5\).
03

Interpret the result

Since the value of x is -5, this means that there was a 5-pound decrease in weight during the first two weeks of the diet. #b. Create a formula for change in quantity#
04

Define the variables

Let \(F\) represent the final value, \(I\) represent the initial value, and \(C\) represent the change in quantity.
05

Write the formula

Use the given equation from part a as a guide, we can write a formula to calculate the change in a quantity: \(C = F - I\).
06

Interpret the formula

This formula calculates the change in quantity by subtracting the initial value from the final value. It can be applied to any situation where we need to find the change in a certain quantity, such as weight, distance, or temperature.

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