SOLUTION: Victoria goes to a store and buys an item that costs xx dollars. She has a coupon for 40% off, and then a 5% tax is added to the discounted price. Write an expression in terms of x

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Question 1209555: Victoria goes to a store and buys an item that costs xx dollars. She has a coupon for 40% off, and then a 5% tax is added to the discounted price. Write an expression in terms of xx that represents the total amount that Victoria paid at the register.
Found 4 solutions by ikleyn, math_tutor2020, timofer, greenestamps:
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
Victoria goes to a store and buys an item that costs xx dollars. She has a coupon for 40% off,
and then a 5% tax is added to the discounted price. Write an expression in terms of xx
that represents the total amount that Victoria paid at the register.
~~~~~~~~~~~~~~~~~~~~~~~~~~ 


    an expression in terms of xx 
    that represents the total amount 
    that Victoria paid at the register is   (1-0.4)xx + 0.05*(1-0.4)xx = 0.6xx + 0.05*0.6xx = 0.63xx.    ANSWER

Solved.

-------------------

Simple things should be done in simple way.

Then they become even simpler than they were before.

Otherwise, they will become more complicated than they were before,
which is not desirable.




Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

I'll assume that xx is a typo and it should be x.

x = cost of the item in dollars

The coupon saves her 40%, so she pays the remaining 60%
60% of x = 0.60x = amount she pays before tax is applied.

The 5% tax will bump the price up to 1.05*0.60x = 0.63x dollars.
The 1.05 can be thought of as 1+0.05 = 100% + 5% = 105%
Anything over 100% increases the price, which is why tax is associated with such a percentage.

Alternatively you can think of it like this: 0.60x+0.05*0.60x = 0.60x+0.03x = 0.63x
The 0.60x portion is what she pays before tax, and 0.05*0.60x = 0.03x is the tax itself.


Answer: 0.63x
Answer by timofer(104)   (Show Source): You can put this solution on YOUR website!
(1) Buy an item for x dollars
(2) Coupon 40% off
(3) Pay 5% tax on the remaining part paid


Do what you want with this to make the expression as you want it.
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


It is a very bad practice in algebra to use "xx" as a "variable" to represent a number. "xx" in algebra means x times x.

So let's use just "x" to represent the original price.

(1) Get 40% off --> the price gets multiplied by (100-40) = 60%, or 0.6.

(2) 5% tax is added to the discounted price --> the discounted price gets multiplied by (100+5) = 105%, or 1.05.

The amount that Victoria paid:

(x)(0.6)(1.05) = 0.63x

ANSWER: 0.63x
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