Huang has a coupon that gives him 20% off all items purchased. He buys 3 shirts that each cost the same amount, and he pays with a $100 bill. Which expression represents the amount of change Huang should receive? Check all that apply. 100 – (0.2(3x)) 100 – (0.8(3x)) 100 – (1 – 0.2)(3x) (100 – 1 – 0.2)(x + x + x) 100 – (0.8x + 0.8x + 0.8x)

We are told that Huang has a coupon that gives him 20% off all items purchased. He buys 3 shirts that each cost the same amount, and he pays with a $100 bill.

Let x be the price of each shirt, therefore, price of 3 shirts will be 3x.

Using coupon he will get 20% off on 3 shirts, which means that he will pay 80% of 3x.

[tex]\text{80 percent of 3 shirts}=\frac{80}{100}\times 3x[/tex]

[tex]\text{80 percent of 3 shirts}=0.80\times 3x[/tex]

Now let us subtract price of 3 shirts from $100 to find the amount Huang will receive as change.

[tex]\text{Amount of change that Huang will receive}=100-(0.80\times 3x)=[/tex]

Now let us see which of the given expression matches with our expression.

1. [tex]100-(0.2(3x))[/tex]

In our 1st expression 20% of 3x is being subtracted from 100, while amount that Huang will spent on purchasing 3 shirts is 80% of 3x, therefore, 1st expression is not correct.

2. [tex]100-(0.8(3x))[/tex]

We can see that 2nd expression is same as our expression, therefore, 2nd option is the correct choice.

3. [tex]100-(1-0.2)(3x)[/tex]

Upon subtracting 0.2 from 1 our expression will simplify as:

[tex]100-(0.8(3x))[/tex]

Therefore, 3rd option is the correct choice.

4. [tex](100-1-0.2)(x+x+x)[/tex]

Upon simplifying our expression we will get,

[tex](98.8)(3x)[/tex]

We can see that expression is not matching with our expression, therefore, 4th option is not correct.

5. [tex]100-(0.8x+0.8x+0.8x)[/tex]

Upon factoring out 0.8 from our expression we will get,

[tex]100-(0.8(x+x+x))[/tex]

[tex]100-(0.8(3x))[/tex]

Therefore, our 5th option is also a correct choice.