Answer :
To determine which situation corresponds to the equation [tex]\(0.35(t + \$850) = \$339.50\)[/tex], we can analyze each situation one by one. Here’s a detailed step-by-step solution for each scenario:
1. Rainy's neighbor's fence:
- Rainy’s share is 35% of the total cost (materials + labor).
- Given: 35% of [tex]\(t + \$850\)[/tex] equals \[tex]$339.50. - This exactly matches the given equation \(0.35(t + \$[/tex]850) = \[tex]$339.50\). 2. Manuel’s tire discount: - Manuel gets a 35% discount. - Total savings from the discount is \$[/tex]339.50.
- To find the original cost that gives this saving: [tex]\(0.35 \times (\text{4 tires cost + t}) = \$339.50\)[/tex].
- This does not match the given equation directly since it involves calculating the pre-discount price.
3. Monica’s gown and shoes:
- The store offers a 35% discount on the gown which can be used to buy shoes.
- The gown costs \[tex]$850. - 35% of \$[/tex]850 is [tex]\(0.35 \times 850 = \$297.50\)[/tex].
- This doesn't match the given equation because it only involves the cost of the gown, not additional labor costs.
4. Julie’s tuition:
- After paying [tex]\(t\)[/tex], Julie still owes 35% of the total \[tex]$850. - 35% of \$[/tex]850 is [tex]\(0.35 \times 850 = \$297.50\)[/tex], which means the remaining amount would be \[tex]$297.50. - This doesn’t match since it doesn’t fit the structure of the equation \(0.35(t + \$[/tex]850) = \[tex]$339.50\). 5. Chase’s donation: - Chase's donation puts the total fundraiser at \$[/tex]339.50, or 35% of their target of \[tex]$850. - This implies \(0.35 \times 850 = \$[/tex]297.50\), which would need Chase to donate the rest.
- This again does not match the structure of the equation.
Given the analysis, the situation that correctly fits the equation [tex]\(0.35(t + \$850) = \$339.50\)[/tex] is:
Rainy's neighbor asked her to pay 35% of the cost based on the portion of the fence that ran between their houses, resulting in an amount of \[tex]$339.50 for materials costing \$[/tex]850 plus labor costs, [tex]\(t\)[/tex].
Thus, the corresponding situation is:
Situation 1: Rainy’s neighbor's fence.
1. Rainy's neighbor's fence:
- Rainy’s share is 35% of the total cost (materials + labor).
- Given: 35% of [tex]\(t + \$850\)[/tex] equals \[tex]$339.50. - This exactly matches the given equation \(0.35(t + \$[/tex]850) = \[tex]$339.50\). 2. Manuel’s tire discount: - Manuel gets a 35% discount. - Total savings from the discount is \$[/tex]339.50.
- To find the original cost that gives this saving: [tex]\(0.35 \times (\text{4 tires cost + t}) = \$339.50\)[/tex].
- This does not match the given equation directly since it involves calculating the pre-discount price.
3. Monica’s gown and shoes:
- The store offers a 35% discount on the gown which can be used to buy shoes.
- The gown costs \[tex]$850. - 35% of \$[/tex]850 is [tex]\(0.35 \times 850 = \$297.50\)[/tex].
- This doesn't match the given equation because it only involves the cost of the gown, not additional labor costs.
4. Julie’s tuition:
- After paying [tex]\(t\)[/tex], Julie still owes 35% of the total \[tex]$850. - 35% of \$[/tex]850 is [tex]\(0.35 \times 850 = \$297.50\)[/tex], which means the remaining amount would be \[tex]$297.50. - This doesn’t match since it doesn’t fit the structure of the equation \(0.35(t + \$[/tex]850) = \[tex]$339.50\). 5. Chase’s donation: - Chase's donation puts the total fundraiser at \$[/tex]339.50, or 35% of their target of \[tex]$850. - This implies \(0.35 \times 850 = \$[/tex]297.50\), which would need Chase to donate the rest.
- This again does not match the structure of the equation.
Given the analysis, the situation that correctly fits the equation [tex]\(0.35(t + \$850) = \$339.50\)[/tex] is:
Rainy's neighbor asked her to pay 35% of the cost based on the portion of the fence that ran between their houses, resulting in an amount of \[tex]$339.50 for materials costing \$[/tex]850 plus labor costs, [tex]\(t\)[/tex].
Thus, the corresponding situation is:
Situation 1: Rainy’s neighbor's fence.
