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Answer :
Sure, I'd be happy to help explain how to solve the problem step by step:
### Part a: Determine the Monthly Rent for a 1,500 Square Foot Apartment
1. Understand the Equation: The linear regression equation given is [tex]\( y = 1.165x + 615.23 \)[/tex], where [tex]\( x \)[/tex] represents the square footage, and [tex]\( y \)[/tex] represents the monthly rental price.
2. Plug in the Square Footage: You're asked to determine the rent for an apartment with 1,500 square feet. So you'll substitute [tex]\( x = 1500 \)[/tex] into the equation.
3. Calculate the Rent:
[tex]\[
y = 1.165 \times 1500 + 615.23
\][/tex]
4. Result: After performing the calculation, the monthly rent for an apartment that has 1,500 square feet is approximately [tex]$2,362.73.
### Part b: Determine if Jacob Can Afford the Rent
1. Calculate Affordable Rent Based on Income:
- Jacob has a monthly income of $[/tex]8,000.
- The recommendation is to spend no more than 28% of the monthly gross income on housing.
- Calculate 28% of Jacob's monthly income:
[tex]\[
\text{Maximum Affordable Rent} = 0.28 \times 8000
\][/tex]
2. Result: Jacob can afford to spend up to [tex]$2,240.00 on rent per month.
3. Compare the Rent:
- The calculated rent for the 1,500 square foot apartment is $[/tex]2,362.73.
- Compare this with the maximum affordable rent of [tex]$2,240.00.
4. Conclusion: Since $[/tex]2,362.73[tex]$ exceeds $[/tex]2,240.00$, this means Jacob cannot afford this rental based on the 28% guideline for spending on housing.
I hope this explanation helps you understand how to arrive at the answers for both parts of the question!
### Part a: Determine the Monthly Rent for a 1,500 Square Foot Apartment
1. Understand the Equation: The linear regression equation given is [tex]\( y = 1.165x + 615.23 \)[/tex], where [tex]\( x \)[/tex] represents the square footage, and [tex]\( y \)[/tex] represents the monthly rental price.
2. Plug in the Square Footage: You're asked to determine the rent for an apartment with 1,500 square feet. So you'll substitute [tex]\( x = 1500 \)[/tex] into the equation.
3. Calculate the Rent:
[tex]\[
y = 1.165 \times 1500 + 615.23
\][/tex]
4. Result: After performing the calculation, the monthly rent for an apartment that has 1,500 square feet is approximately [tex]$2,362.73.
### Part b: Determine if Jacob Can Afford the Rent
1. Calculate Affordable Rent Based on Income:
- Jacob has a monthly income of $[/tex]8,000.
- The recommendation is to spend no more than 28% of the monthly gross income on housing.
- Calculate 28% of Jacob's monthly income:
[tex]\[
\text{Maximum Affordable Rent} = 0.28 \times 8000
\][/tex]
2. Result: Jacob can afford to spend up to [tex]$2,240.00 on rent per month.
3. Compare the Rent:
- The calculated rent for the 1,500 square foot apartment is $[/tex]2,362.73.
- Compare this with the maximum affordable rent of [tex]$2,240.00.
4. Conclusion: Since $[/tex]2,362.73[tex]$ exceeds $[/tex]2,240.00$, this means Jacob cannot afford this rental based on the 28% guideline for spending on housing.
I hope this explanation helps you understand how to arrive at the answers for both parts of the question!
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