ACT Math : How to find the sale price

Study concepts, example questions & explanations for ACT Math

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Example Questions

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Example Question #31 : Sale Prices

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?

Round to the nearest .

Possible Answers:

Correct answer:

Explanation:

We can apply our formula, if we remember to first divide by :

 ---> 

Thus, our rounded answer is .

 

Example Question #32 : How To Find The Sale Price

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 video game is normally priced at . If the game is subsequently purchased for , what was the discount, as a percent, on the purchase?

Possible Answers:

There is not enough information to answer the question.

Correct answer:

Explanation:

To find the discount as a percent, simply divide the sale price by the original price, and multiply by  (to convert from a decimal to a percent).

 --> 

Thus, the game was purchased on a  discount.

Example Question #33 : How To Find The Sale Price

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 steak dinner at Steaks 'R Us is normally priced at . The restaurant gives a discount to a preferred customer, and they eat for . What was the discount, as a percent, on the dinner?

Possible Answers:

Correct answer:

Explanation:

To find the discount as a percent, simply divide the sale price by the original price, and multiply by  (to convert from a decimal to a percent).

 --> 

Thus, the game was purchased on approximately  discount.

Example Question #31 : How To Find The Sale Price

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.

Company A sells bicycles normally costing  for . Company B sells bicycles normally costing  for . Which company offers a greater discount, as a percentage?

Possible Answers:

Company B

There is not enough information to answer the question.

Company A

Both companies offer the same percentage discount.

Correct answer:

Company B

Explanation:

Here we are looking to solve our equation for . We need only to solve each equation for , with the bigger  representing the bigger percent discount.

 ---> 

For Company A: 

For Company B:

Thus, Company B offers the greater discount by percentage.

Example Question #35 : How To Find The Sale Price

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.

Maria makes cakes for big events, like weddings and graduations. She sells a cake that costs her  to make for a total of . The customer later purchases another cake identical to the first one, and Maria gives a discount, selling the second cake for only . What percent of Maria's profits did she sacrifice for the customer? 

Possible Answers:

Correct answer:

Explanation:

It is a mistake to assume that we must calculate the profit percentage of each sale to find the answer to this problem. All we need to do to solve is to compare the ratio of the new sale's absolute amount to the old sale's absolute amount, and we will have our percentage.

So, Maria gave up approximately  of her profits on the second cake.

Example Question #36 : How To Find The Sale Price

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.

Chen can choose from one of three deals for a new weight set: He can get  off of a  set, or  off of a  set, or  off of a  set. Assuming the quality of sets is identical, which discount results in the least expensive set for Chen?

Possible Answers:

The  set at  off.

The  set at  off.

There is not enough information to answer the question.

The  set at  off.

All of these offer the same final price.

Correct answer:

The  set at  off.

Explanation:

To find the best final sale amount, we simply apply our equation three times:

For the first weight set:

For the second weight set:

For the third weight set:

So, the least expensive weight set is the  set at  off.

Example Question #37 : How To Find The Sale Price

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.

John buys a car at a  discount, and pays . Susan buys a car at a  discount, and pays . Romeo buys a car at a  discount, and pays . Before any discount was applied, who bought the most expensive car?

Possible Answers:

Romeo.

John.

Susan.

There is not enough information to answer the question.

All three cars were the same price before the discount.

Correct answer:

All three cars were the same price before the discount.

Explanation:

To find the original price of the car, substitute our known values into the equation for each car, then solve for .

For the first car:

 ---> 

For the second car:

 ---> 

For the third car:

 ---> 

So, all three cars initially cost the same (although Susan appears to be the superior negotiator!)

Example Question #38 : How To Find The Sale Price

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 certain product sells for  dollars at full price, but can be purchased at  off for each additional unit past the first that is purchased, to a maximum of  off each unit if  or more are purchased at one time.

Which equation represents the price, with discount, of a purchase of  units of this product?

Possible Answers:

Correct answer:

Explanation:

Purchasing  units entitles us to the maximum  discount on each unit, so we simply calculate the cost of  units at  off:

Example Question #39 : How To Find The Sale Price

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.

Save-All Foods has a coupon matching program where customers can bring in any competitor's coupon and have the cash or percent off amount on the coupon face matched at their location. A customer brings in a coupon for  off a gallon of milk from another grocery store. If the milk at Save-All Foods normally costs /gallon, and the milk at the competitor costs /gallon, how much money does the customer save on the final price of milk by using the coupon matching program?

Round to the nearest cent.

Possible Answers:

/gallon

/gallon

/gallon

/gallon

/gallon

Correct answer:

/gallon

Explanation:

To find the answer here, simply calculate our equation for discounts using each store's price, then find the difference in final cost.

For the competitor:

 ---> 

For Save-All Foods:

 ---> 

So, the customer saves /gallon by using the coupon at Save-All Foods.

Example Question #31 : How To Find The Sale Price

Mark wants to buy a new television for football season.  The TV is currently on a  sale. Mark also has a store loyalty card which gives him an extra  off. The final price of the TV is what percentage off of the original cost?

Possible Answers:

Correct answer:

Explanation:

When dealing with an unknown price in a percentage price, it is always beneficial to simply choose a starting price.  The easiest number to choose is always  To find how much the TV costs after the initial sale, we need to do .  Since this is a percentage reduction problem, we need to subtract the percentage form the whole. Then, we need to calculate the final price of the TV with the extra discount:  .  To find out the percentage difference between the original and final price, we can simply subtract the two prices (which is why it is easiest to start with the number  

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