Questions: To make fudge-like brownies, a person bakes a brownie mix for 9 minutes less than the baking time suggested on the box. Let r be the suggested baking time (in minutes) and a be the actual baking time (in minutes). Complete parts (a) through (d). a. Find an equation that describes the relationship between r and a Assume that a is the dependent variable. [Hint: Find the equation by creating a table of values for r and a] An equation that describes the relationship between r and a is a = r - 9 (Type an expression using r as the variable.) b. Perform a unit analysis of the equation found in part (a) Choose the correct answer below O. In the equation, the units on both sides are not the same so the equation is correct O B. In the equation, the units on both sides are the same so the equation is correct.

To make fudge-like brownies, a person bakes a brownie mix for 9 minutes less than the baking time suggested on the box. Let r be the suggested baking time (in minutes) and a be the actual baking time (in minutes). Complete parts (a) through (d). a. Find an equation that describes the relationship between r and a Assume that a is the dependent variable. [Hint: Find the equation by creating a table of values for r and a] An equation that describes the relationship between r and a is a = r - 9 (Type an expression using r as the variable.) b. Perform a unit analysis of the equation found in part (a) Choose the correct answer below O. In the equation, the units on both sides are not the same so the equation is correct O B. In the equation, the units on both sides are the same so the equation is correct.
Transcript text: To make fudgelike brownies, a person bakes a brownie mix for 9 minutes less than the baking time suggested on the box. Let r be the suggested baking time (in minutes) and a be the actual baking time (in minutes). Complete parts (a) through (d). a. Find an equation that describes the relationship between r and a Assume that a is the dependent varable. [Hint: Find the equation by creating a table of values for $r$ and a ] An equation that describes the relationship between r and a is $\mathrm{a}=\mathrm{r}-9$ (Type an expression using $r$ as the variable.) b. Perform a unit analysis of the equation found in part (a) Choose the correct answer below O. In the equation, the units on both sides are not the same so the equation is correct O B. In the equation, the units on both sides are the same so the equation is correct.
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Solution

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Solution Steps

To solve the given problem, we need to follow these steps:

  1. Part (a): Identify the relationship between the suggested baking time \( r \) and the actual baking time \( a \). The problem states that the actual baking time is 9 minutes less than the suggested baking time. Therefore, the equation is \( a = r - 9 \).

  2. Part (b): Perform a unit analysis to ensure that the units on both sides of the equation are consistent. Since both \( r \) and \( a \) represent time in minutes, the units on both sides of the equation are the same.

Step 1: Establish the Relationship

The problem states that the actual baking time \( a \) is 9 minutes less than the suggested baking time \( r \). This relationship can be expressed mathematically as: \[ a = r - 9 \]

Step 2: Example Calculation

To illustrate this relationship, let's consider an example where the suggested baking time \( r \) is 30 minutes. Using the equation from Step 1: \[ a = 30 - 9 = 21 \] Thus, the actual baking time \( a \) is 21 minutes.

Step 3: Unit Analysis

Next, we perform a unit analysis on the equation \( a = r - 9 \). Both \( r \) and \( a \) represent time in minutes. Therefore, the units on both sides of the equation are consistent: \[ \text{In the equation, the units on both sides are the same so the equation is correct.} \]

Final Answer

The relationship between the suggested baking time \( r \) and the actual baking time \( a \) is given by: \[ \boxed{a = r - 9} \] For the example provided, if \( r = 30 \): \[ \boxed{a = 21} \] The unit analysis confirms that the equation is valid.

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