Today, everything at a store is on sale. The store offers a 20% discount. a) The regular price of a T-shirt is $18. What is the discount price?

b) If the regular price of an item is dollars, what is the discount price in dollars? Write an expression.

c) The discount price of a hat is $18. What is the regular price?

a. $14.4

b. $18 • .2 = $3.6

c. $21.6

Step-by-step explanation:

a. Make the 20% a decimal, and multiply by the regular price. Then, subtract that and you'll get the discounted price.

18 • .2 = 3.6

18-3.6 = $14.4

b. Use the equation multiplying the 20% as a fraction here.

c. Multiply $18 by .2 (the discount). Then, add that to the discount price ($18).

18 • .2 = 3.6

3.6 + 18 = $21.6

step-by-step explanation:

30% of $420 is 0.30($420) = $126 and $420 + $126 = $546.

or, 130% of $420 is 1.3($420) = $546.

notice that this is not the $600 original list price with which we started.

why doesn't this work?

the method does not work because 30% of $420 is not the same amount as the 30% of $600. it may seem obvious when stated this way, but it is a very common error made on problems of this type. we cannot just use the same percent and get back to the original amount because we are taking that percent of a different value.

to work problems of this type correctly, it is generally best to write an equation for the situation and then solve.

example: since (100% – 30%)(original price) = (sale price)

70% of the   (original price) is $420.

0.7x   = 420

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x = 600

the original cost was $600.

we may also solve this problem using the two-step method. working the problem in two steps requires us to use more algebra skills. we have to know that x = 1x (identity property of multiplicationtext annotation indicator) and that 1x – 0.3x = 0.7x (subtracting like terms). then we solve the problem as follows:

(original price) – 30%(original price) = sale price

x – 0.3x = 420

0.7x = $420

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x = 600

the original cost was $600.  

note that with both of the above methods we do obtain the correct original amount.

example: after a 5% pay raise, hermione is earning $22,680 per year. what was she earning before the pay raise?

105% of (original salary) = current salary

1.05x = 22,680

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x = 21,600

hermione earned $21,600 per year before the pay raise.

this is an example so maybe you will get how to at least do it!