To determine which expression correctly represents the total amount of change Alexis should receive when she buys [tex]\( x \)[/tex] boxes of cereal costing [tex]$3 each and pays with a $[/tex]20 bill, let's break down the problem step-by-step.
1. Calculate the total cost of the cereal:
- Each box of cereal costs [tex]$3.
- Alexis buys \( x \) boxes.
- Therefore, the total cost of the cereal is \( 3x \) dollars.
2. Subtract the total cost from the amount paid:
- Alexis pays with a $[/tex]20 bill.
- The amount of change she receives is the amount she paid minus the total cost of the cereals.
- Thus, the change Alexis should receive is [tex]\( 20 - 3x \)[/tex] dollars.
We now compare this with the given expressions:
1. Expression 1: [tex]\( 20 - 3x \)[/tex]
- This expression correctly subtracts the total cost of the cereal from the amount paid, giving the correct change.
2. Expression 2: [tex]\( (3 - 20)x \)[/tex]
- This expression implies subtracting 20 from 3 first, which gives a negative number multiplied by [tex]\( x \)[/tex]. This does not correctly represent the situation.
3. Expression 3: [tex]\( 3x - 20 \)[/tex]
- This expression calculates the cost of the cereal and then subtracts 20, which does not correctly reflect the change received.
4. Expression 4: [tex]\( (20 - 3)x \)[/tex]
- This expression subtracts 3 from 20 first, which results in 17, and then multiplies by [tex]\( x \)[/tex], which is incorrect.
Given these evaluations, the correct expression that represents the total amount of change Alexis should receive is:
[tex]\( 20 - 3x \)[/tex].
Therefore, the correct answer is:
[tex]\[ \boxed{20 - 3x} \][/tex]
