All ACT Math Resources
Example Questions
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 , whereÂ
 is the discounted price,Â
 is the original price, andÂ
 is the percent to be discounted in decimal form.
Company A sells bicycles normally costing  forÂ
. Company B sells bicycles normally costingÂ
 forÂ
. Which company offers a greater discount, as a percentage?
There is not enough information to answer the question.
Company A
Company B
Both companies offer the same percentage discount.
Company B
Here we are looking to solve our equation for . We need only to solve each equation forÂ
, with the biggerÂ
 representing the bigger percent discount.
 --->Â
For Company A:Â
For Company B:
Thus, Company B offers the greater discount by percentage.
Example Question #1301 : Act Math
To find the sale price for a single item or group of like items, one can use the equation , whereÂ
 is the discounted price,Â
 is the original price, andÂ
 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 onlyÂ
. What percent of Maria's profits did she sacrifice for the customer?Â
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 #141 : Percentage
To find the sale price for a single item or group of like items, one can use the equation , whereÂ
 is the discounted price,Â
 is the original price, andÂ
 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 aÂ
 set, orÂ
 off of aÂ
 set, orÂ
 off of aÂ
 set. Assuming the quality of sets is identical, which discount results in the least expensive set for Chen?
All of these offer the same final price.
There is not enough information to answer the question.
The  set atÂ
 off.
The  set atÂ
 off.
The  set atÂ
 off.
The  set atÂ
 off.
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 atÂ
 off.
Example Question #142 : Percentage
To find the sale price for a single item or group of like items, one can use the equation , whereÂ
 is the discounted price,Â
 is the original price, andÂ
 is the percent to be discounted in decimal form.
John buys a car at a  discount, and paysÂ
. Susan buys a car at aÂ
 discount, and paysÂ
. Romeo buys a car at aÂ
 discount, and paysÂ
. Before any discount was applied, who bought the most expensive car?
Romeo.
There is not enough information to answer the question.
All three cars were the same price before the discount.
Susan.
John.
All three cars were the same price before the discount.
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:
 --->Â
For the second car:
 --->Â
For the third car:
 --->Â
So, all three cars initially cost the same (although Susan appears to be the superior negotiator!)
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 , whereÂ
 is the discounted price,Â
 is the original price, andÂ
 is the percent to be discounted in decimal form.
A certain product sells for  dollars at full price, but can be purchased atÂ
 off for each additional unit past the first that is purchased, to a maximum ofÂ
 off each unit ifÂ
 or more are purchased at one time.
Which equation represents the price, with discount, of a purchase of  units of this product?
Purchasing  units entitles us to the maximumÂ
 discount on each unit, so we simply calculate the cost ofÂ
 units atÂ
 off:
Example Question #1302 : Act Math
To find the sale price for a single item or group of like items, one can use the equation , whereÂ
 is the discounted price,Â
 is the original price, andÂ
 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 costsÂ
/gallon, and the milk at the competitor costsÂ
/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.
/gallon
/gallon
/gallon
/gallon
/gallon
/gallon
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:
 --->Â
For Save-All Foods:
 --->Â
So, the customer saves /gallon by using the coupon at Save-All Foods.
Example Question #144 : Percentage
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 extraÂ
 off. The final price of the TV is what percentage off of the original cost?
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 doÂ
. Â 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: Â
. Â 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 numberÂ
Â
Example Question #231 : Arithmetic
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?
Â
Â
$128
$272
$160
$208
$240
$208
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.
Â
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.Â
Â
Finally, do the subtraction of the original price minus the price Max paid: $400 – $192 = $208.
Â
Â
Example Question #1 : How To Find Amount Of Profit
Patrice earns $75 per day. Ron earns $350 per week. How many days does Patrice have to work to earn more than what Ron earns in 5 weeks?
Â
24
23
20
25
24
Find out how much Ron earns in 5 weeks ($1750). Divide by Patrice’s daily wage (23.3333 days). Patrice needs to work at least 24 days. At 23 days, she will only have earned $1725, falling $25 short of Ron’s 5 week earnings.
Â
Â
Example Question #231 : Arithmetic
A business launches a new product that produces $x in sales its first year. Sales in the second year are double the first, and the third year has sales four times as large as the first year. If 2nd year sales were $12 million, how much in total sales was produced over the 3 year period?
Â
Â
$40 million
$48 million
$42 million
$36 million
$42 million
Write out an equation. Total sales = T = x +2x + 4x
If 2x = 12, x = 6
T = 6 + 12 + 24 = $42 million
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