To determine which of the given expressions is not a valid way to calculate how much money Jenna is spending, we need to evaluate each option in relation to the problem statement: Jenna is buying 4 new shirts at \$20 each.
1. Expression: [tex]\(2n + 2n + 2n + 2n = \infty\)[/tex]
- Let's analyze this step-by-step:
- It's given that [tex]\(n = 4\)[/tex] (the number of shirts).
- Breaking down the expression, it translates to [tex]\(2 \times 4 + 2 \times 4 + 2 \times 4 + 2 \times 4\)[/tex].
- Simplifying each term, we get [tex]\(8 + 8 + 8 + 8 = 32\)[/tex], not [tex]\(\infty\)[/tex].
- The equation itself seems formulated incorrectly with respect to the context, and the result [tex]\(\infty\)[/tex] is incorrect.
Therefore, this expression is not a valid way to represent the total cost.
2. Expression: [tex]\(20 \cdot 4 = 80\)[/tex]
- Here, [tex]\(20\)[/tex] represents the price per shirt, and [tex]\(4\)[/tex] represents the number of shirts.
- Calculating [tex]\(20 \times 4\)[/tex], we indeed get [tex]\(80\)[/tex].
This expression correctly calculates the total cost.
3. Expression: [tex]\(\frac{x}{4} = 80\)[/tex]
- This equation suggests that when some number [tex]\(x\)[/tex] is divided by 4, the result is 80.
- To find [tex]\(x\)[/tex], we multiply both sides of the equation by 4:
- [tex]\(x = 80 \times 4\)[/tex]
- [tex]\(x = 320\)[/tex]
- When interpreted correctly, it is internally consistent, but it doesn't directly calculate the total cost of the shirts based on the given problem.
This math doesn't directly represent Jenna's situation but is not inherently incorrect.
4. Expression: [tex]\(4 \times 20 = 80\)[/tex]
- Again, [tex]\(4\)[/tex] is the number of shirts and [tex]\(20\)[/tex] is the price per shirt.
- Calculating [tex]\(4 \times 20\)[/tex], we get [tex]\(80\)[/tex].
This is also a valid way to represent the total cost correctly.
With these evaluations:
- The first expression [tex]\(2n + 2n + 2n + 2n = \infty\)[/tex] does not correctly represent the situation and results in an incorrect value.
Therefore, the expression that is NOT a valid way to write a calculation for how much money Jenna is spending is [tex]\(2n + 2n + 2n + 2n = \infty\)[/tex].
