Ratios, Rates, And Proportions

1. Do the ratios 15/4 and 26/7 form a proportion?

Yes, they're equal!

No, they're not!

The ratios 15/4 and 26/7 do not form a proportion because they are not equal. In order for two ratios to form a proportion, their cross products must be equal. However, when we calculate the cross products of 15/4 and 26/7, we get 15*7 = 105 and 4*26 = 104, which are not equal. Therefore, the given ratios do not form a proportion.

Explanation

The ratios 15/4 and 26/7 do not form a proportion because they are not equal. In order for two ratios to form a proportion, their cross products must be equal. However, when we calculate the cross products of 15/4 and 26/7, we get 15*7 = 105 and 4*26 = 104, which are not equal. Therefore, the given ratios do not form a proportion.

2. Megan traveled to her grandma's house, which is 200 miles away. It took her about 5 hours to get there. What was her average speed in miles per hour?

40 miles per hour

200/5 miles per hour

.025 miles per hour

4 miles per hour

Megan traveled 200 miles in 5 hours, so her average speed can be calculated by dividing the total distance by the total time taken. 200/5 equals 40, so her average speed was 40 miles per hour.

Explanation

Megan traveled 200 miles in 5 hours, so her average speed can be calculated by dividing the total distance by the total time taken. 200/5 equals 40, so her average speed was 40 miles per hour.

3. How many dogs are in the dog park if there are 24 people, and there are 2 dogs for every 3 people?

18 dogs

16 dogs

6 dogs

36 dogs

If there are 24 people in the dog park and there are 2 dogs for every 3 people, we can calculate the number of dogs by dividing the total number of people by 3 and then multiplying it by 2. So, (24/3) * 2 = 16 dogs.

Explanation

If there are 24 people in the dog park and there are 2 dogs for every 3 people, we can calculate the number of dogs by dividing the total number of people by 3 and then multiplying it by 2. So, (24/3) * 2 = 16 dogs.

4. Solve the proportion:

45 / 5 = s / 7

S = 63

S = 32

S = 49

S = 70

To solve the proportion, we can cross multiply. So, 45 multiplied by 7 is equal to s multiplied by 5. This gives us 315 = 5s. To isolate s, we divide both sides of the equation by 5. Therefore, s = 63.

Explanation

To solve the proportion, we can cross multiply. So, 45 multiplied by 7 is equal to s multiplied by 5. This gives us 315 = 5s. To isolate s, we divide both sides of the equation by 5. Therefore, s = 63.

5. Write the ratio as a fraction in simplest form. 28 to 12

3/7

14/6

7/3

2/1

The ratio 28 to 12 can be simplified by dividing both numbers by their greatest common divisor, which is 4. 28 divided by 4 is 7, and 12 divided by 4 is 3. Therefore, the simplified fraction is 7/3.

Explanation

The ratio 28 to 12 can be simplified by dividing both numbers by their greatest common divisor, which is 4. 28 divided by 4 is 7, and 12 divided by 4 is 3. Therefore, the simplified fraction is 7/3.

6. An 8 oz. glass of orange juice contains 72 milligrams of vitamin C. If I wanted 60 milligrams if vitamin C, how many oz. of juice would I need to drink?

6 2/3 ounces of juice

9.6 ounces of juice

540 ounces of juice

To find out how many ounces of juice are needed to obtain 60 milligrams of vitamin C, we can set up a proportion. We know that 8 ounces of juice contain 72 milligrams of vitamin C. So, we can set up the proportion: 8/72 = x/60, where x represents the unknown number of ounces of juice. By cross-multiplying and solving for x, we find that x = (8 * 60) / 72 = 6 2/3 ounces of juice. Therefore, to obtain 60 milligrams of vitamin C, one would need to drink 6 2/3 ounces of juice.

Explanation

To find out how many ounces of juice are needed to obtain 60 milligrams of vitamin C, we can set up a proportion. We know that 8 ounces of juice contain 72 milligrams of vitamin C. So, we can set up the proportion: 8/72 = x/60, where x represents the unknown number of ounces of juice. By cross-multiplying and solving for x, we find that x = (8 * 60) / 72 = 6 2/3 ounces of juice. Therefore, to obtain 60 milligrams of vitamin C, one would need to drink 6 2/3 ounces of juice.

7. Which box of cereal is the better buy?

$2.50 for 12 oz.

$3.60 for 18 oz.

$4.95 for 24 oz.

The better buy is $3.60 for 18 oz because it offers the lowest price per ounce compared to the other options. To calculate the price per ounce, divide the cost of the cereal by the number of ounces. In this case, $3.60 divided by 18 oz equals $0.20 per ounce. The other options have higher prices per ounce: $2.50 divided by 12 oz equals $0.21 per ounce, and $4.95 divided by 24 oz equals $0.21 per ounce. Therefore, the $3.60 for 18 oz option is the most cost-effective.

Explanation

The better buy is $3.60 for 18 oz because it offers the lowest price per ounce compared to the other options. To calculate the price per ounce, divide the cost of the cereal by the number of ounces. In this case, $3.60 divided by 18 oz equals $0.20 per ounce. The other options have higher prices per ounce: $2.50 divided by 12 oz equals $0.21 per ounce, and $4.95 divided by 24 oz equals $0.21 per ounce. Therefore, the $3.60 for 18 oz option is the most cost-effective.

8. There is a recipe for cake that calls for 4 1/4 cups of flour. If this recipe serves 6 people, then how much flour is needed to serve a party of 14 people? Round to the nearest tenth.

10.5 cups of flour

19.7 cups of flour

9.9 cups of flour

1.8 cups of flour

If the recipe serves 6 people and calls for 4 1/4 cups of flour, we can calculate the amount of flour needed per person by dividing the total amount of flour by the number of people. 4 1/4 cups of flour divided by 6 people equals approximately 0.708 cups of flour per person. To find out how much flour is needed for a party of 14 people, we can multiply the amount of flour per person (0.708 cups) by the number of people (14). This gives us approximately 9.9 cups of flour needed to serve a party of 14 people.

Explanation

If the recipe serves 6 people and calls for 4 1/4 cups of flour, we can calculate the amount of flour needed per person by dividing the total amount of flour by the number of people. 4 1/4 cups of flour divided by 6 people equals approximately 0.708 cups of flour per person. To find out how much flour is needed for a party of 14 people, we can multiply the amount of flour per person (0.708 cups) by the number of people (14). This gives us approximately 9.9 cups of flour needed to serve a party of 14 people.

9. Cassie and her friends ate 2 pizzas in 10 minutes. What is the rate per minute?

5 pizzas per minute

.5 pizzas per minute

1 pizza per minute

.2 pizzas per minute

The correct answer is .2 pizzas per minute. This means that Cassie and her friends ate 0.2 pizzas every minute. Since they ate 2 pizzas in 10 minutes, we can divide 2 by 10 to find the rate per minute, which is 0.2.

Explanation

The correct answer is .2 pizzas per minute. This means that Cassie and her friends ate 0.2 pizzas every minute. Since they ate 2 pizzas in 10 minutes, we can divide 2 by 10 to find the rate per minute, which is 0.2.

10. Write the ratio as a fraction in simplest form. 8 meters : 240 centimeters

1 / 30

10 / 3

800 / 240

8 / 240

To find the ratio as a fraction in simplest form, we need to convert both the meters and centimeters to the same unit. Since there are 100 centimeters in 1 meter, we can convert 8 meters to centimeters by multiplying it by 100, resulting in 800 centimeters. Therefore, the ratio of 8 meters to 240 centimeters can be simplified to 800/240, which further simplifies to 10/3.

Explanation

To find the ratio as a fraction in simplest form, we need to convert both the meters and centimeters to the same unit. Since there are 100 centimeters in 1 meter, we can convert 8 meters to centimeters by multiplying it by 100, resulting in 800 centimeters. Therefore, the ratio of 8 meters to 240 centimeters can be simplified to 800/240, which further simplifies to 10/3.