Alg 1 (5): Unit Conversions

12 1) Identify the unit you're converting from In this case, it's 90 chicken sandwiches 2) Identify the unit you're converting to (usually found in the last sentence) In this case, it's the number of packages. 3) Use dimensional analysis to convert the units 90 chicken sandwiches * (3/4 pounds / 1 chicken sandwich) * (1 package / 6 pounds) = 11.25 packages It's not possible to buy just 0.25 of a package, so we need to round up to 12.

From The College Panda ACT Math: Advanced Guide and Workbook (p. 28)¹: A catering company needs to make 90 chicken sandwiches for a local event. Each chicken sandwich will contain 3/4 pounds of chicken. If the catering company buys its chicken in 6-pound packages, what is the minimum number of packages of chicken needs to buy for the event?

$27.00

From The College Panda ACT Math: Advanced Guide and Workbook (p. 29)¹: At the printing center, Sara made one copy of a 150-page manuscript and two copies of a 40-page article. She was charged a total of $41.40. If the printing center charges for copies at a fixed rate per page, how much did Sara have to pay to copy the 150-page manuscript?

11

From The College Panda ACT Math: Advanced Guide and Workbook (p. 31)¹: A lightbulb manufacturer is delivering an order of 6,000 lightbulbs using large boxes and small boxes. A large-size box can fit a maximum of 800 lightbulbs. A small-size box can fit a maximum of 350 lightbulbs. If the manufacturer will use 3 large-size boxes, what is the maximum number of small-size boxes needed to deliver all the lightbulbs?

2.16 * 10⁻⁵ Use dimensional analysis to convert 21.6 microseconds to seconds: 21.6 microseconds * (1 second / 1,000,000 microseconds) = 21.6/1,000,000 seconds = 0.0000216 seconds Recall: How to convert into scientific notation: 1) Rewrite the number so that there is only 1 digit before the decimal 0.0000216 seconds → 2.16 2) Multiply your answer by 10ⁿ Where n = the number of times you needed to move the decimal If you moved the decimal to the left, n is positive If you moved the decimal to the right, n is negative For 0.0000216, we needed to move the decimal 5 times to the right to get 2.16 So n = -5 Therefore, our answer is: 2.16 * 10⁻⁵

From The College Panda ACT Math: Advanced Guide and Workbook (p. 37)¹: There are 1,000,000 microseconds in a second. In scientific notation, 21.6 microseconds is equivalent to how many seconds?

416

From The College Panda ACT Math: Advanced Guide and Workbook (p. 42)¹: A box at the supermarket can hold 6 oranges each. Each orange costs the supermarket 20 cents. Given that the supermarket has a budget of $500 to stock oranges, how many boxes will the supermarket be able to completely fill?

168

From The College Panda ACT Math: Advanced Guide and Workbook (p. 42)¹: A tree grows at an average rate of 2.8 inches per month. By approximately how many inches does the tree grow over 5 years?

$105

From The College Panda ACT Math: Advanced Guide and Workbook (p. 42)¹: Joanna is paid $30 per hour to sew buttons on shirts. If she sews 840 buttons at the rate of 4 buttons per minute, how much will she be paid?

48

From The College Panda ACT Math: Advanced Guide and Workbook (p. 43)¹: A car can travel 1 mile in 1 minute and 15 seconds. At this rate, how many miles can the car travel in 1 hour?

12.5

From The College Panda ACT Math: Advanced Guide and Workbook (p. 43)¹: A recipe for 12 servings requires 5 cups of water. About how many cups of water are required for 30 servings?

B) (4b)/(7a)

From The College Panda ACT Math: Advanced Guide and Workbook (p. 44)¹: The Russell family has a pet dog. The dog eats a cans of pet food every 4 days. At this rate, how many weeks will it take the dog to eat b cans of pet food? A) (4a)/(7b) B) (4b)/(7a) C) (7a)/(4b) D) (7b)/(4a) E) (28b)/(a)

9

From The College Panda ACT Math: Advanced Guide and Workbook (p. 44)¹: Tom drives 30 miles at an average rate of 50 miles per hour. If Leona drives at an average rate of 40 miles per hour, how many more minutes will it take her to travel the same distance?

3 days 18 hours

From The College Panda ACT Math: Advanced Guide and Workbook (p. 45)¹: A recipe recommends fermenting a certain type of vegetable for 5 hours per ounce of the vegetable's weight. Based on this recipe, how long should an 18-ounce vegetable of this type be fermented? A) 2 days 12 hours B) 2 days 18 hours C) 3 days 6 hours D) 3 days 12 hours E) 3 days 18 hours

10 + (10m)/3

From The College Panda ACT Math: Advanced Guide and Workbook (p. 45)¹: A recycling machine processes 10 plastic bottles in 3 minutes. At this rate, how many plastic bottles does the recycling machine process in 3 + m minutes? A) 10/3 + m B) 10/3 + m/3 C) 10/3 + 10/(3m) D) 10 + m/3 E) 10 + (10m)/3

5

From The College Panda ACT Math: Advanced Guide and Workbook (p. 45)¹: A squirrel has gathered enough acorns to last 20 days if it eats 6 acorns each day. How many acorns should it eat each day if the same number of acorns is to last 24 days?

20

From The College Panda ACT Math: Advanced Guide and Workbook (p. 45)¹: An empty aquarium can hold 18,000 gallons of water when full. It will be filled by 5 hoses, each of which pumps 3 gallons of water per minute. How many hours will it take to fill the aquarium?

20

From The College Panda ACT Math: Advanced Guide and Workbook (p. 45)¹: In a cycling race, Hugo finished a course 2.4 miles long in 7 minutes and 12 seconds. About how many miles per hour did he average for the race?

18 weeks

From The College Panda ACT Math: Advanced Guide and Workbook (p. 45)¹: In one week, a master tailor can make 15 suits whereas his apprentice can only make one-third as many. If they alternate weeks (i.e. the master works this week and the apprentice works the next), how many weeks would it take them to make 180 suits altogether?

$2

From The College Panda ACT Math: Advanced Guide and Workbook (p. 45)¹: Sarah wants to buy 30 staplers. Shop A sells staplers at 6 for $10. Shop B sells staplers at 5 for $8. How many dollars will Sarah save by going to the store with the better deal?

$910

From The College Panda ACT Math: Advanced Guide and Workbook (p. 45)¹: The total charge for a hotel room includes a fixed upfront fee plus a daily rate for the room. If the total charge for the room is $400 for a 4-day stay and $570 for a 6-day stay, what is the total charge for a 10-day stay?

18

From The College Panda ACT Math: Advanced Guide and Workbook (p. 46)¹: A baking company hires employees to make and package cookies. Each employee assigned to baking can make 30 cookies per hour. Each employee assigned to packaging can package 4 cookies every 12 minutes. The company currently has 15 employees who are all assigned to baking. How many employees should be hired and assigned to packaging so that the company makes and packages the same number of cookies in 1 hour.

30

From The College Panda ACT Math: Advanced Guide and Workbook (p. 46)¹: Megan and Kristie are working together to grade 65 essays. Megan can grade 5 essays per hour and Kristie can grade 6 essays per hour. If Megan starts grading first and Kristie joins her two hours later, how many essays will Kristie have graded by the time they finish?

54

From The College Panda ACT Math: Advanced Guide and Workbook (p. 47)¹: The instructions for coconut milk call for 2 cups of coconut juice and 3 cups of whole milk. Under these instructions, how many cups of whole milk will be needed to make 90 cups of coconut milk?

6 red blocks.

From The College Panda ACT Math: Advanced Guide and Workbook (p. 48)¹: When Pamela fills a box with only red blocks, 36 of them fit. When she fills the sam box with only blue blocks, 48 of them fit. If she then empties out the box and puts 40 blue blocks inside, what is the greatest possible number of red blocks she can fit in the remaining space inside the box?

90

From The College Panda ACT Math: Advanced Guide and Workbook (p. 50)¹: A blueprint drawing of a rectangular room is 10 inches wide and 8 inches long. The actual room is 25 feet wide. If the blueprint drawing is proportional to the actual room, what is the perimeter of the room, in feet?

12 red beads

From The College Panda ACT Math: Advanced Guide and Workbook (p. 50)¹: Clarissa makes beaded necklaces in two different sizes. A large necklace consists of 24 blue beads and 36 red beads. A small necklace consists of a total of 20 beads in the same ratio of blue beads and red beads as the large necklace. How many red beads does Clarissa put in the same necklace?

125

From The College Panda ACT Math: Advanced Guide and Workbook (p. 50)¹: The time it takes to transfer a file is directly proportional to the file's size. If a 280 megabyte file takes 50 seconds to transfer, how many seconds will it take to transfer a 700 megabyte file?

45

From The College Panda ACT Math: Advanced Guide and Workbook (p. 51)¹: A recipe that makes 5 servings of salad dressing requires 2 cups of balsamic vinegar and 2/3 cup of sesame oil. Brianna has 20 cups of balsamic vinegar and 6 cups of sesame oil. If she maintains the same ratio of ingredients, what is the greatest number of servings of salad dressing she can make?

2 and 5/8

From The College Panda ACT Math: Advanced Guide and Workbook (p. 51)¹: Jody is a pharmacist who is tasked with mixing a solution for a new medication. The original recipe calls for 3 and 1/2 milliliters of water and 1 and 3/4 milligrams of calcium phosphate. Jody will use the entire contents of a beaker that contains 5 and 1/4 milliliters of water and will use the same ratio of ingredients called for in the original recipe. How many milligrams of calcium phosphate will Jody use? A) 2 and 3/8 B) 2 and 1/2 C) 2 and 5/8 D) 3 and 1/4 E) 3 and 1/2

Using a process called dimensional analysis It's a method of converting from one unit to another by multiplying fractions. For example, if you want to convert 120 km/s into mi/hr... 1) Convert the km to miles: 120 km/s * (1.6 mi/km) Notice how I multiplied the number by a fraction, which contains the conversion rate between miles and km's The km's "cross cancel out", so you're left with: 192 mi/s 2) Convert s to min, then min to hr: 192 mi/s * (60 s/min) * (60 min/hr) = 691,200 mi/hr

How do you convert from one unit to another? Use your knowledge to convert 120 km/s into mi/hr