GOAL - find a missing term in a proportion (direct, inverse, and partitive) M6NS-Ilb-133 to solve problems involving direct proportion, partitive proportion, and inverse proportion in different contexts such as distance, rate, and time using appropriate strategies and tools. M6NS-Ilc-134
TASK : You will create a short instructional step by step text on how to solve proportion problems.
1. On a map, two cities are 6 inches apart. If 2 inches on the map represents 25 kilometers, how far apart are the cities?
2. It takes 4 men 6 hours to repair a road. How long will it take 8 men to do the job if they work at the same rate?
3. In a class of 40, the ratio of boys to girls is 3:5. How many are girls? How many are boys?
TASK : You will create a short instructional step by step text on how to solve proportion problems.
1. On a map, two cities are 6 inches apart. If 2 inches on the map represents 25 kilometers, how far apart are the cities?
2. It takes 4 men 6 hours to repair a road. How long will it take 8 men to do the job if they work at the same rate?
3. In a class of 40, the ratio of boys to girls is 3:5. How many are girls? How many are boys?
Answers & Comments
Verified answer
Answer:
1. The cities are 75 kilometers apart.
2. It will take 12 hours for 8 men to do the job.
3. There are 24 boys and 16 girls in the class.
Step-by-step explanation:
Sure! Here are the straight solutions to the three proportion problems:
1. On a map, two cities are 6 inches apart. If 2 inches on the map represents 25 kilometers, how far apart are the cities?
To find the distance between the cities, we can set up a proportion:
2 inches / 6 inches = 25 kilometers / x kilometers
Cross-multiplying, we get:
2 inches * x kilometers = 6 inches * 25 kilometers
Simplifying, we have:
2x = 150
Dividing both sides by 2, we find:
x = 75
Therefore, the cities are 75 kilometers apart.
2. It takes 4 men 6 hours to repair a road. How long will it take 8 men to do the job if they work at the same rate?
To find the time it takes for 8 men to do the job, we can set up a proportion:
4 men / 8 men = 6 hours / x hours
Cross-multiplying, we get:
4 men * x hours = 8 men * 6 hours
Simplifying, we have:
4x = 48
Dividing both sides by 4, we find:
x = 12
Therefore, it will take 8 men 12 hours to do the job.
3. In a class of 40, the ratio of boys to girls is 3:5. How many are girls? How many are boys?
To find the number of girls and boys in the class, we can set up a proportion:
3 boys / 5 girls = x boys / 40 students
Cross-multiplying, we get:
3 boys * 40 students = 5 girls * x boys
Simplifying, we have:
120 = 5x
Dividing both sides by 5, we find:
x = 24
Therefore, there are 24 boys and 40 - 24 = 16 girls in the class.