# Solving Problems by Finding Equivalent Ratios

Videos and solutions to help Grade 6 students learn how to solve problems by finding equivalent ratios.

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Lesson Plans and Worksheets for Grade 6
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### New York State Common Core Math Grade 6, Module 1, Lesson 5

Lesson 5 Student Outcomes

• Students use tape diagrams to find an equivalent ratio when given the part-to-part ratio and the total of those two quantities.
• Students use tape diagrams to find an equivalent ratio when given the part-to-part ratio and the difference between those two quantities.
• Students make the connection between the constant, c, in the definition of equivalent ratios and the value of the unit in the tape diagram used to solve ratio problems.
• Students use tape diagrams to solve problems when given a ratio between two quantities and a change to those quantities that changes the ratio.

NYS Math Grade 6, Module 1, Lesson 5, Example 1

A County Superintendent of Highways is interested in the numbers of different types of vehicles that regularly travel within his county. In the month of August, a total of 192 registrations were purchased for passenger cars and pickup trucks at the local Department of Motor Vehicles (DMV). The DMV reported that in the month of August, for every 5 passenger cars registered, there were 7 pickup trucks registered. How many of each type of vehicle were registered in the county in the month of August?
a. Using the information in the problem, write four ratios and describe the meaning of each.
b. Make a tape-diagram that represents the quantities in the ratios that you wrote.
c. How many equal-sized parts does the tape diagram consist of?
d. What total quantity does the tape diagram represent?
e. What value does each individual part of the tape diagram represent?
f. How many of each type of vehicle were registered in August? NYS Math Module 1 Grade 6 Lesson 5 Example 2

The Superintendent of Highways is further interested in the numbers of commercial vehicles that frequently use the county’s highways. He obtains information from the Department of Motor Vehicles for the month of September and finds that for every 14 non-commercial vehicles, there were 5 commercial vehicles. If there were 108 more non- commercial vehicles than commercial vehicles, how many of each type of vehicle frequently use the county’s highways during the month of September?

NYS Math Module 1 Grade 6 Lesson 5 Exercises 1, 2

1. The ratio of the number of people who own a smartphone to the number of people who own a flip phone is 4:3. If 500 more people own a smartphone than a flip phone, how many people own each type of phone?

2. Sammy and David were selling water bottles to raise money for new football uniforms. Sammy sold 5 water bottles for every 3 water bottles David sold. Together they sold 160 water bottles. How many did each boy sell? NYS Math Module 1 Grade 6 Lesson 5 Exercise 3

3. Ms. Johnson and Ms. Siple were folding report cards to send home to parents. The ratio of the number of report cards Ms. Johnson folded to the number of report cards Ms. Siple folded is 2:3. At the end of the day, Ms. Johnson and Ms. Siple folded a total of 300 report cards. How many did each person fold? NYS Math Module 1 Grade 6 Lesson 5 Exercise 4

4. At a country concert, the ratio of the number of boys to the number of girls is 2:7. If there are 250 more girls than boys, how many boys are at the concert?

Problem Set
1. Last summer, at Camp Okey-Fun-Okey, the ratio of the number of boy campers to the number of girl campers was 8:7. If there were a total of 195 campers, how many boy campers were there? How many girl campers?

2. The student–to–faculty ratio at a small college is 17:3. The total of students and faculty is 740. How many faculty members are there at the college? How many students?

3. The Speedy Fast Ski Resort has started to keep track of the number of skiers and snowboarders who bought season passes. The ratio of the number of skiers who bought season passes to the number of snowboarders who bought season passes is 1:2. If 1250 more snowboarders bought season passes than skiers, how many snowboarders and how many skiers bought season passes?

4. The ratio of the number of adults to the number of students at the prom has to be 1:10. Last year there were 477 more students than adults at the prom. If the school is expecting the same attendance this year, how many adults have to attend the prom?

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