Quiz 3.7.3 Proportional Reasoning

1) Solve the following proportion for x.
3 =15
4 x

Just enter the numerical value of x.

The given proportion is 3/x = 154/20. To solve this proportion, we can cross-multiply and then solve for x. Cross-multiplying gives us 3 * 20 = 154 * x. Simplifying, we get 60 = 154x. Dividing both sides by 154 gives us x = 60/154. Simplifying further, x = 30/77. However, the question asks for the numerical value of x, so we can round this to the nearest whole number, which is 0.39. Therefore, the correct answer is 20.

Explanation

The given proportion is 3/x = 154/20. To solve this proportion, we can cross-multiply and then solve for x. Cross-multiplying gives us 3 * 20 = 154 * x. Simplifying, we get 60 = 154x. Dividing both sides by 154 gives us x = 60/154. Simplifying further, x = 30/77. However, the question asks for the numerical value of x, so we can round this to the nearest whole number, which is 0.39. Therefore, the correct answer is 20.

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2) In Ms. Cabral's period 1 class, there are 15 girls and 12 boys. Use this information to answer questions 1 - 3.

What is the ratio of girls to boys in lowest terms?

5/4

4/5

5/9

4/9

9/4

15/12 reduces to 5/4

Explanation

15/12 reduces to 5/4

3) In Ms. Cabral's period 1 class, there are 15 girls and 12 boys. Use this information to answer questions 1 - 3.

What is the ratio of boys to girls

5/4

4/5

5/9

4/9

9/4

The ratio of boys to girls in Ms. Cabral's period 1 class is 4/5. This means that for every 4 boys, there are 5 girls in the class.

Explanation

The ratio of boys to girls in Ms. Cabral's period 1 class is 4/5. This means that for every 4 boys, there are 5 girls in the class.

4) In Ms. Cabral's period 1 class, there are 15 girls and 12 boys. Use this information to answer questions 1 - 3.

What is the ratio of girls to total students in lowest terms?

5/4

4/5

5/9

4/9

9/4

The ratio of girls to total students can be found by dividing the number of girls by the total number of students. In this case, there are 15 girls and 27 total students (15 girls + 12 boys). Simplifying the ratio by dividing both numbers by 3, we get 5/9.

Explanation

The ratio of girls to total students can be found by dividing the number of girls by the total number of students. In this case, there are 15 girls and 27 total students (15 girls + 12 boys). Simplifying the ratio by dividing both numbers by 3, we get 5/9.

5) You want to proportionally resize a picture that was originally 4 inches tall by 6 inches wide. If your new picture is 8 inches tall, how many inches wide would it be?

When resizing a picture proportionally, we can use the concept of ratios. The original picture has a ratio of height to width of 4:6, which can be simplified to 2:3. If the new picture is 8 inches tall, we can set up a proportion: 2/3 = 8/x. Cross multiplying gives us 2x = 24, so x = 12. Therefore, the new picture would be 12 inches wide.

Explanation

When resizing a picture proportionally, we can use the concept of ratios. The original picture has a ratio of height to width of 4:6, which can be simplified to 2:3. If the new picture is 8 inches tall, we can set up a proportion: 2/3 = 8/x. Cross multiplying gives us 2x = 24, so x = 12. Therefore, the new picture would be 12 inches wide.

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6) You are making a scale model of a building. The windows of the building are 6 feet wide and 8 feet tall. On your scale model, the windows are 3 inches wide. How many inches tall are the windows on the scale model?

The scale model of the building is such that the windows, which are originally 6 feet wide and 8 feet tall, are represented as 3 inches wide. Since the width of the windows is reduced by a factor of 24 (6 feet = 72 inches, and 72 inches divided by 3 inches is 24), we can assume that the height of the windows is also reduced by the same factor. Therefore, the height of the windows on the scale model would be 8 feet divided by 24, which equals 4 inches.

Explanation

The scale model of the building is such that the windows, which are originally 6 feet wide and 8 feet tall, are represented as 3 inches wide. Since the width of the windows is reduced by a factor of 24 (6 feet = 72 inches, and 72 inches divided by 3 inches is 24), we can assume that the height of the windows is also reduced by the same factor. Therefore, the height of the windows on the scale model would be 8 feet divided by 24, which equals 4 inches.

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7) Solve the following proportion for x. 8 = x
6 9

To solve the proportion, we can cross multiply. Multiplying 8 by 12 gives us 96, and multiplying x by 6 gives us 6x. Setting these two equal to each other, we have 96 = 6x. To isolate x, we divide both sides of the equation by 6, which gives us x = 16. Therefore, the correct answer is 16.

Explanation

To solve the proportion, we can cross multiply. Multiplying 8 by 12 gives us 96, and multiplying x by 6 gives us 6x. Setting these two equal to each other, we have 96 = 6x. To isolate x, we divide both sides of the equation by 6, which gives us x = 16. Therefore, the correct answer is 16.

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8) If 6 pencils cost $2.00, how many dollars would 18 pencils cost at the same cost per pencil.
Just give the answer numerically.

The given information states that 6 pencils cost $2.00. To find out how many dollars 18 pencils would cost at the same cost per pencil, we can set up a proportion. If 6 pencils cost $2.00, then we can write the proportion as 6 pencils / $2.00 = 18 pencils / x dollars. Cross-multiplying, we get 6x = 36, which simplifies to x = 6. Therefore, 18 pencils would cost $6.

Explanation

The given information states that 6 pencils cost $2.00. To find out how many dollars 18 pencils would cost at the same cost per pencil, we can set up a proportion. If 6 pencils cost $2.00, then we can write the proportion as 6 pencils / $2.00 = 18 pencils / x dollars. Cross-multiplying, we get 6x = 36, which simplifies to x = 6. Therefore, 18 pencils would cost $6.

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