Question

An electrician plans to install solar panels on a rectangular section of roof with an area of 69 m^2. Tyriq said 69 ÷ 7 1/10 could represent the length of the section if the roof is 7 1/10 m across. Corbin said 69 ÷ 7 1/10 could represent the number of solar panels that would fit if each panel was 7 1/10 m long. Whose interpretation makes sense in this context? a) Tyriq's only b) Corbin's only c) Both Tyriq's and Corbin's

Answer 1

Both Tyriq's and Corbin's interpretations make sense in this context.

Step-by-step explanation:

To determine whose interpretation makes sense in this context, let's break down the problem. The student wants to install solar panels on a rectangular section of roof with an area of 69 m^2. Tyriq says 69 ÷ 7 1/10 could represent the length of the section if the roof is 7 1/10 m across, while Corbin says 69 ÷ 7 1/10 could represent the number of solar panels that would fit if each panel was 7 1/10 m long.

To check Tyriq's interpretation, we can calculate the length of the section by dividing the area by the width: 69 ÷ (7 1/10) = 9.7 m. This means the length of the section would be approximately 9.7 meters.

To check Corbin's interpretation, we can calculate the number of solar panels that would fit by dividing the area by the length of each panel: 69 ÷ (7 1/10) = 9.7 panels. This means approximately 9.7 solar panels would fit.

Since both calculations result in approximately 9.7, both Tyriq's and Corbin's interpretations make sense in this context.

Answer 2

The correct answer is: a) Tyriq's only

Let's analyze both interpretations:

Tyriq's interpretation:
`\( (69)/(7(1)/(10)) \)` represents the length of the section if the roof is 7 1/10 m across.

Corbin's interpretation:
`\( (69)/(7(1)/(10)) \)` represents the number of solar panels that would fit if each panel was 7 1/10 m long.

To check which interpretation makes sense, we need to look at the units.

The area of the roof is given in square meters (m²), and the length of the section is in meters (m). So, we are looking for a length value.

Let's perform the division:
`\( (69)/(7(1)/(10)) \)`.

`\[ (69)/(7(1)/(10)) = (69)/((71)/(10)) \]`

To divide by a fraction, multiply by its reciprocal:

`\[ (69)/((71)/(10)) \cdot (10)/(1) = (690)/(71) \]`

This result represents the length of the section in meters. Therefore, Tyriq's interpretation makes sense in this context.