Okay, let's tackle the problem step-by-step.
Let’s denote the cost of each shirt as [tex]\( x \)[/tex]. Since Huang buys 3 shirts, the total cost of the shirts is [tex]\( 3x \)[/tex].
In addition to the shirts, Huang buys a pair of pants that costs [tex]$12. Therefore, the total amount Huang spends is the cost of the shirts plus the cost of the pants.
We can write this as:
\[ \text{Total Cost} = 3x + 12 \]
Given that Huang pays with a \$[/tex]100 bill, the amount of change he should receive is the difference between the amount he paid and the total cost. Therefore, the expression for the change he should receive is:
[tex]\[ \text{Change} = 100 - (3x + 12) \][/tex]
Now, let’s analyze the given options to see which expressions represent the amount of change:
1. [tex]\( 100 - (12(3x)) \)[/tex]:
- This expression is incorrect because it incorrectly multiplies the number of shirts (3) and the cost of pants (12).
2. [tex]\( 100 - (3x + 12) \)[/tex]:
- This expression is correct and matches our derived expression.
3. [tex]\( (100 - 12) - 3x \)[/tex]:
- This expression is also correct. It simplifies the $100 by subtracting the cost of the pants first, then the cost of the shirts:
[tex]\[ (100 - 12) - 3x = 88 - 3x \][/tex]
4. [tex]\( (100 - 12)(x + x + x) \)[/tex]:
- This expression is incorrect because it implies a multiplication rather than a subtraction.
5. [tex]\( 100 - (x + x + x) - 12 \)[/tex]:
- This expression is correct. It first subtracts the total shirt cost (as [tex]\( x + x + x \)[/tex] = [tex]\( 3x \)[/tex]) and then the cost of the pants:
[tex]\[ 100 - (3x) - 12 \][/tex]
Hence, the three expressions that represent the amount of change Huang should receive are:
[tex]\[ 100 - (3x + 12) \][/tex]
[tex]\[ (100 - 12) - 3x \][/tex]
[tex]\[ 100 - (x + x + x) - 12 \][/tex]
