Comparing and Scaling Test

Name: ______Date: ______Class Period: ______page 1 of 8

Comparing and Scaling Preview:

I. Define each term and give an example of how each is used: A. Ratio: The ratio of two numbers r and s is written r/s where r is divided by s.

B. Proportion: Two equivalent ratios

C. Percent: A ratio r/s where s = 100. “Per” = “For each” [as in miles per hour]. “cent” = “100” [as in cents in a dollar, years in a century, or centimeters in a meter.] Name: ______Date: ______Class Period: ______page 2 of 8

II. Jenny is making a game with a spinner. She wants to use the following ratios: Blue: Green = 3:2 and Red:Blue = 2:1

a) How many sections of each color should she use? Assume 2 sections of Green. Then there will be 2 sections of green, 3 sections of blue, and 6 sections of red [3 blue, so 2 x 3 = 6 which should be red] …11 sections total.

If you assume 4 sections of green, you get: 4 green; 6 blue; 12 red…22 sections total.

b)How many degrees should she make the blue section be? There are 11 sections total (2 + 3 + 6 = 11). 3 are blue, so 3/11 should be blue. There are 360 degrees in a circle. This gives us a proportion : 3 d = 11 360 3* 360 1080 2 d = = = 98 11 11 11 2 the blue section should be 98 degrees (about 98.2). 11

alternate questions: a) What percent of the circle should be blue? 3/11=p/100 b) What percent of the circle should be red? c) What percent of the circle should be green? d) What percent of the circle should be yellow? Name: ______Date: ______Class Period: ______page 3 of 8

II. For each problem: A. Write a proportion to represent the situation. B. Show the equation(s) or step(s) you use to answer the question. C. Be sure to answer the question. Be sure to use units where appropriate.

1. There are two doorways into the fun house. The doors are similar rectangles. The tall door is 9 feet high and 5 feet wide. The short door is 4 feet high. How wide is the short door?

Proportion (2pts) Equation/work (2pts) Answer (units) (2pts) tall short 9 ft 4 ft = The short door is 2 2/9 Height 9 ft 4 ft 5 ft x Wide 5 ft x feet wide…or 2 feet and 4 ft * 5 ft 20 2 9 ft 4 ft x = = ft = 2 ft 2 2/3 inches. = 9 ft 9 9 2 x in 5 ft x ft = 9 12in 2 *12 24 8 2 x = = = = 2 9 9 3 3

Note: If you need help setting up the proportion, use the box diagrams! Name: ______Date: ______Class Period: ______page 4 of 8

2. There are 96 pretzels in a 20-ounce bag of chocolate covered pretzels. a) Write and solve a proportion to find the number of chocolate covered pretzels in a 24-ounce bag. Proportion (2pts) Equation/work (2pts) Answer (units) (2pts) Given find Q1 96 p 96 pz * 24oz There are about 115 pretzels in a (pretzels) p pz = 24 ounce bag. Q2 20oz (ounces) 20 24 2304 pz 96 pz p pz p pz = = 115.2 pz = 20 20oz 24oz NOTE: Keep UNITS in your problem to be sure that you are comparing SIMILAR quantities. Add rows or columns, if you need to!

b) What is the number of pretzels per ounce? Proportion (2pts) Equation/work (2pts) Answer (units) (2pts) 96 pz p pz = 20oz 1 oz reading note: “ounce” implies only 1 ounce! d c) How many ounces does each pretzel weigh? This means that you are looking for 2 OUNCES PER PRETZEL…number of pretzels = 1! Proportion (2pts) Equation/work (2pts) Answer (units) (2pts) 20oz z oz = 96 pz 1 pz Name: ______Date: ______Class Period: ______page 5 of 8

d) Which is the better value: a 20-ounce bag for $2.49 or a 30-ounce bag for $3.69?

There are three ways to answer this question: 1)ounces per dollar (higher number is better value)

2)dollars per ounce (lower number is better value)

3)How much is it to buy 60 ounces of pretzels each way?

Either way, convert BOTH prices into the same unit (oz/$ or $/oz) and compare them!

Proportion (2pts) Equation/work (2pts) Answer (units) (2pts)

Bag 20 30 size Dollars 2.49 3.69 Cost 2.49÷20= 3.69÷30=0.123 per 0.1245 ounce

.1245<.12301~|- Name: ______Date: ______Class Period: ______page 6 of 8

3. A roller coaster covers a distance of 2 miles in 40 seconds. a) What is its speed in miles per minute? Proportion (2pts) Equation/work (2pts) Answer (units) (2pts) 2mi x = 40sec 60sec

1 min  60 sec

b) What is its speed in miles per hour? Proportion (2pts) Equation/work (2pts) Answer (units) (2pts) 3mi b = 1min 60 min Note: 3 miles in 1 minute is the ANSWER to question a above. This sets up the possibility of a CASCADE error!

Be VERY careful when using the answer to one question to find the answer to another question!

c) How many miles can it go in 5 minutes? Proportion (2pts) Equation/work (2pts) Answer (units) (2pts) 3mi c = 1min 5min

d) How many minutes will it take to go 15 miles? Proportion (2pts) Equation/work (2pts) Answer (units) (2pts) 3mi 15 mi = 1min d min Name: ______Date: ______Class Period: ______page 7 of 8

e) Write an equation to find a time (t) in minutes to cover any distance (d). [HINT: t and d will BOTH be in your answer! Your answer should start with “t=” ]

3mi d mi = 1min t d mi*1min t = 3mi d mi*1min t = 3 mi d t = min 3 Name: ______Date: ______Class Period: ______page 8 of 8

4. Kelsey makes $164 in two weeks at her job with the traveling carnival. Reading note: This implies that Kelsey gets paid every two weeks! b) At that rate, how much does she make in a 52-week year? Proportion (2pts) Equation/work (2pts) Answer (units) (2pts) $164 x = 2wks 52wks

c) If she works 12 hours per week, how much does she make per hour? Proportion (2pts) Equation/work (2pts) Answer (units) (2pts)

$82 x $164 $82 $82 = = ¾¾® 12hr 1hr 2wks 1wk 12hr x = $82 x = 12hr 1hr

Kelsey is saving to buy a car that will cost $2200. How many weeks will she have to work to save enough money to buy the car? Proportion (2pts) Equation/work (2pts) Answer (units) (2pts) $82 $2200 She will have to work about $82 $2200 = 27 weeks. 1week w weeks [26.9…Note: you cannot round = 1week * $2200 w = this DOWN to 26.8 because she 1week w weeks $82 will not have enough money!]

w = 26.82926 NOTE: If the question asked “How long before she can buy the car?” 28 is a better answer because the problem implies that she gets paid every two weeks, so it would be an even number of weeks before she received the paycheck which would allow her to purchase the car!