ACT Math - How to find the sale price

Max wants to buy a couch at The Furniture Store. The couch he is considering had been marked on sale for 20% off and was selling for $320. The day he comes in to buy the couch, it has been marked down an additional 40% off of the sale price. What is the difference in the original price of the couch and what Max paid for the couch?

$128

$160

$208

$240

$272

Explanation

First find the original price of the couch. If $320 represents the price after taking 20% off, then $320 = 80% of the original price. To find the original price, divide (320) / (0.8) = 400.

Then find the "additional sale" price. The couch has been marked down an additional 40% from the sale price of $320. Since "40% off" means that you pay 60% of what you would have, multiply the sale price of $320 by the 60% that Max pays. $320 * 0.6 = $192.

Finally, do the subtraction of the original price minus the price Max paid: $400 – $192 = $208.

To find the sale price for a single item or group of like items, one can use the equation , where is the discounted price, is the original price, and is the percent to be discounted in decimal form.

A pair of headphones normally sells for . If the headphones are on a -off discount, how expensive are they?

Explanation

To find the new sale price, apply the discount to the original price in decimal form.

--->

A store buys a new line of dresses for $15.00 each. They increase this price by 40% when they sell the dresses in the store. This week, the dresses are on sale for 20% off. What is the price of one dress this week?

$\dpi{100} \small $ 16.80$

$\dpi{100} \small $ 18.00$

$\dpi{100} \small $ 21.00$

$\dpi{100} \small $ 12.00$

$\dpi{100} \small $ 17.50$

Explanation

The price of one dress is now $16.80. The original price was $15.00. When the dresses were sold in the store, the price was increased by 40%, to $21.00

( $15+15\times 0.4=21$ )

Then, the price was decreased by 20%, to $16.80.

( $21-21\times 0.2=16.8$ )

It might be tempting to just increase the original price by 20%, but the percent increase and the percent decrease must be performed together.

A dress is priced at $375 and a pair of shoes are $150. If they are both on sale for 30% off, what is price of purchasing them both on sale?

$367.50

$157.50

$525.50

$281.50

$393.75

Explanation

$375 + $150 = $525

Sale price is 30% off or (0.3)($525) = $157.50

Subtract the discount from the initial price: $525 – $157.50 = $367.50

To find the sale price for a single item or group of like items, one can use the equation , where is the discounted price, is the original price, and is the percent to be discounted in decimal form.

A car ordinarily sells for , but a savvy consumer walks out having paid only of that price. How much did the customer pay?

Explanation

Applying our equation from above:

--->

So, the customer paid , or of the original price.

Julie only has to spend on a prom dress on tax free weekend. She has narrowed her search down to her four favorites: a red dress costing but marked down a blue dress costing marked down , a yellow dress costing marked down , and a purple dress costing marked down . Which dress can Julie buy?

yellow dress

red dress

blue dress

purple dress

She cannot afford any of the dresses.

Explanation

This is a percentages problem. To find the price of an item on sale by a certain percentage, you subtract that percentage decimal from 1.0, and multiply that number by the cost of the dress. Then, you compare that number to the amount she has to see if she can afford it.

Red dress price=

Blue dress price=

Yellow dress price=

Purple dress price=

Since the yellow dress is the only dress under her total amount of money, that is the only dress she can afford.

To find the sale price for a single item or group of like items, one can use the equation , where is the discounted price, is the original price, and is the percent to be discounted in decimal form.

Some clothes are on sale at off retail. If a customer buys three pairs of jeans for a total of , what was the original price of one pair of jeans?

Explanation

We can apply our formula, but first we should divide the total price by , then fill in what we know:

--->

$P_o = \frac{$ 33}{.6} = $ 55$

So, one pair of jeans without discount costs .

James goes to the store to buy a new pair of shoes. He sees a pair he likes for that are marked off. Ignoring sales tax, how much does James pay for the shoes? Round to the nearest cent.

Explanation

To find how much is remaining after is taken off, subtract from (the total price of the original pair of shoes) and multiply it by the shoe's price.
which rounds to

A shirt was originally , but the manager of the store decided to mark it down by . What is the new cost of the shirt after this?

Explanation

There are two ways to do a question like this. The first is to find out what the markdown is. We do this by multiplying:

to get

Then, you subtract this from to get .

The other way to solve this is to notice that the total cost of the shirt will be only of the original price. Therefore, you can multiply by to get as well.

To find the sale price for a single item or group of like items, one can use the equation , where is the discounted price, is the original price, and is the percent to be discounted in decimal form.

A pack of batteries is on sale for of the normal price. If ten packs cost , what is the non-discounted price of one pack of batteries?