### All ACT Math Resources

## Example Questions

### 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:**

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.

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.

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

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:**

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

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

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:**

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

### Example Question #1 : Profit Margin

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?

**Possible Answers:**

25

20

23

24

**Correct answer:**

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.

### Example Question #1 : Profit Margin

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 2^{nd} year sales were $12 million, how much in total sales was produced over the 3 year period?

**Possible Answers:**

$40 million

$42 million

$36 million

$48 million

**Correct answer:**

$42 million

Write out an equation. Total sales = T = x +2x + 4x

If 2x = 12, x = 6

T = 6 + 12 + 24 = $42 million

### Example Question #1 : Profit Margin

A jewelry designer bought a booth at a local craft fair. She paid $160 for the booth rental for the day. Her necklaces cost $10 to make and she sells them for $50 apiece. If she wants to make at least $1000 profit for the day, how many necklaces must she sell?

**Possible Answers:**

18

29

24

22

20

**Correct answer:**

29

Profit on Necklace = Price – Cost = $50 – $10 = $40

Total Profit = # of Necklaces Sold * $40 – Booth Rental Rate

$1000 Profit = # of Necklaces * $40 – $160

$1160 = # of Necklaces * $40

# Necklaces = 29

### Example Question #1311 : Act Math

A law firm earned $2,000,000 this year in fees. If the firm’s annual operating costs are $1,250,000, what is their profit this year?

**Possible Answers:**

$1,250,000

$250,000

$750,000

$2,000,000

$1,000,000

**Correct answer:**

$750,000

Profit = Total Fees – Operating Costs = $2,000,000 – $1,250,000 = $750,000