Unit 4 Quiz 1 Study Guide ANSWER KEY PDF

## Unit 4 Quiz 1 Study Guide ### Question 1 A preschool has a teacher to student ratio of 2:5. The total number of students and teachers was 56 last year, and is 70 this year. How many students and teachers were there for each of these two years? * **Last Year:** * 40 teachers and 16 student...

## Unit 4 Quiz 1 Study Guide ### Question 1 A preschool has a teacher to student ratio of 2:5. The total number of students and teachers was 56 last year, and is 70 this year. How many students and teachers were there for each of these two years? * **Last Year:** * 40 teachers and 16 students. * $\frac{40}{56} = \frac{5}{7}$ * $\frac{16}{56} = \frac{2}{7}$ * **This Year:** * 50 teachers and 20 students. * $\frac{50}{70} = \frac{5}{7}$ * $\frac{20}{70} = \frac{2}{7}$ **b.** * **Last Year:** * 16 teachers and 40 students. * $\frac{16}{56} = \frac{2}{7}$ * $\frac{40}{56} = \frac{5}{7}$ * **This Year:** * 20 teachers and 50 students. * $\frac{20}{70} = \frac{2}{7}$ * $\frac{50}{70} = \frac{5}{7}$ **c.** * **Last Year:** * 26 teachers and 30 students. * $\frac{26}{56} = \frac{13}{28}$ * $\frac{30}{56} = \frac{15}{28}$ * **This Year:** * 30 teachers and 40 students. * $\frac{30}{70} = \frac{3}{7}$ * $\frac{40}{70} = \frac{4}{7}$ **d.** * **Last Year:** * 14 teachers and 35 students. * $\frac{14}{49} = \frac{2}{7}$ * $\frac{35}{49} = \frac{5}{7}$ * **This Year:** * 10 teachers and 25 students. * $\frac{10}{35} = \frac{2}{7}$ * $\frac{25}{35} = \frac{5}{7}$ ### Question 2 Jose is using 12 brown tiles and 8 white tiles to design a section of an outdoor patio. What ratio compares the number of brown tiles to the total number of tiles in one section? $\frac{12 \text{ brown}}{20 \text{ total}} = \frac{3}{5}$ ### Question 3 The table shows the party affiliation of the 100 senators of the 109th Congress. The ratio of Republicans to Democrats is 5:4. How many senators are Democrats? Independents? | Party Affiliation | Number of Senators | |---|---| | Republican | 55 | | Democrat | 44 | | Independent | 1 | $\frac{5}{x} = \frac{55}{d}$ * $5d = 55x$ * $d = 11x$ 100 - (55 + 44) = 1 ### Question 4 An animal shelter with only dogs and cats has a ratio of cats to dogs that is 9:7. **Part A - What is the ratio of dogs to all animals?** 7:16 **Part B - A second shelter has a ratio of cats to dogs of 6 to 5. If both shelters have 18 cats, which shelter has more dogs?** * **Shelter #1:** * $\frac{9}{x} = \frac{18}{x}$ * $ x=14$ * **Shelter #2:** * $\frac{6}{5} = \frac{18}{x}$ * $x=15$ The second shelter has more dogs. ### Question 5 Complete the ratio table. Then plot the pairs on the coordinate plane. **Ratio Table** | x | y | |---|---| | 2 | 3 | | 4 | 6 | | 6 | 9 | ### Question 6 Cars pass through the intersection at a rate of 32 cars each hour. How many cars pass through the intersection in 5.25 hours? 32 x 5.25 = 168 cars ### Question 7 Jessica is buying several bunches of bananas to make desserts for a fundraiser. She can buy 10 pounds of bananas for $14.90 or 8 pounds of bananas for $12.08. Which is the better buy? Explain. * $14.90 / 10 = $1.49 per pound. * $12.08 / 8 = $1.51 per pound. The 10 pounds for $14.90 is a better buy because it is 2 cents less per pound. ### Question 8 Marie has 8 hours to write a 45-page chapter for her book. Marie writes at a constant speed of 4 pages per hour. Will Marie complete the chapter in time? Explain. 8 hours * 4 pages per hour = 32 pages. Marie will not be able to complete her chapter in only 8 hours. ### Question 9 Jenna walks 12 miles in 5 days. Alex walks 7 miles in 3 days. Who walks more miles per day? Show or explain how you determined your answer. * Jenna: * 12 miles / 5 days = 2.4 miles per day * Alex: * 7 miles / 3 days = 2.3 miles per day Jenna walks more miles per day. ### Question 10 The soccer team raised $300 and the lacrosse team raised $450. How much money did the lacrosse team raise for every $1.00 dollar the soccer team raised? $\frac{450}{300}= $1.50 ### Question 11 There are 28 students in Mr. Flynn's class. The ratio of his students who are in the play to those who are not in the play is 2:5. How many students are in the play? 2 in : 5 not in = 7 total students * 28 students / 7 total students = 4 * 4 * 2 in = 8 students in the play ### Question 12 Kristy rides 6 miles on her bicycle in 40 minutes. Jax rides 4 miles on his bicycle in 30 minutes. Complete the ratio tables for Kristy and Jax. | Kristy | |---|---| | Distance (mi) | Time (min) | | 6 | 40 | | 12 | 80 | | 18 | 120 | | 24 | 160 | | 30 | 200 | | Jax | |---|---| | Distance (mi) | Time (min) | | 4 | 30 | | 8 | 60 | | 12 | 90 | | 16 | 120 | | 20 | 150 | Who has the better rate? Explain. Kristy has the better rate because it took her 10 less minutes to travel 12 miles. ### Question 13 A hair salon uses 4 bottles of shampoo for every 3 bottles of conditioner. Graph this ratio. * **Use your graph to find the number of bottles of conditioner that are used when 16 bottles of shampoo are used.** * 16 bottles of shampoo will use 12 bottles of conditioner.