To address this problem, let us focus on Jackson’s constraints and given information to determine the relevant domain and range.
1. Jackson can use a total of [tex]$120 on his purchase.
2. He plans to buy 2 shirts and 3 pairs of pants.
Let's delve deeper into the problem by breaking it down:
### Domain (Cost of Shirts)
- Jackson wants to buy 2 shirts.
- Let \( x \) represent the total cost of shirts.
- If Jackson spends all his money on shirts, the maximum he can spend is \( \$[/tex]120 \). But since he needs money left over to buy pants, we have to consider a typical balance.
- Given the solution, estimate the most sensible maximum cost for the shirts:
- It would make sense if the combined price of 2 shirts does not exceed half of his budget.
### Range (Cost of Pants)
- Jackson also wants to buy 3 pairs of pants.
- Let [tex]\( y \)[/tex] represent the total cost of the pants.
- After the expenditure on shirts, [tex]\( 120 - x \)[/tex] would be left for the pants.
- Again, given the solution's rationale: if approximately half is spent on pants, this needs balance as well.
### Contextual Calculation
- For Jackson's scenario to stay within budget constraints:
[tex]\[
2 \text{ shirts} + 3 \text{ pairs of pants} \leq 120
\][/tex]
- Thus:
- If [tex]\( 2 \times \text{cost of one shirt} = 60 \)[/tex]
- Therefore,
- Remaining budget: [tex]\( 120 - 60 = 60 \)[/tex]
- For 3 pairs of pants: [tex]\( 60 / 3 = 20 \text{ per pant} \)[/tex]
- So, [tex]\( y \)[/tex] is within this understandable calculated scenario.
### Summarizing:
- Shirts (Domain): [tex]\( 0 \leq x \leq 60 \)[/tex]
- Pants (Range): [tex]\( 0 \leq y \leq 40 \)[/tex]
Thus, the correct answer is:
A. domain: [tex]\( 0 \leq x \leq 60 \)[/tex]
range: [tex]\( 0 \leq y \leq 40 \)[/tex]
