Fundamentals of Ratios: Proportional Calculus Quiz

Since the ratio of boys to girls is 3:5 and there are 24 boys, we can set up a proportion. Let x be the number of girls. The proportion becomes 3/5 = 24/x. Cross-multiplying, we get 3x = 120. Solving for x, we find x = 40. Therefore, there are 40 girls in the class.

To simplify a ratio, divide both values by their greatest common divisor. The greatest common divisor of 24 and 40 is 8. Dividing both values by 8, we get 3:5. Therefore, the simplified ratio of 24:40 is 3:5.

Using the given ratio of cats to dogs (2:5) and the number of cats (20), we can set up a proportion. Let x be the number of dogs. The proportion becomes 2/5 = 20/x. Cross-multiplying, we get 2x = 100. Solving for x, we find x = 50. Therefore, there are 50 dogs in the pet store.

To simplify a ratio, divide both values by their greatest common divisor. The greatest common divisor of 15 and 20 is 5. Dividing both values by 5, we get 3:4. Therefore, the simplified ratio of 15:20 is 3:4.

Using the given ratio of men to women (7:4) and the number of men (28), we can set up a proportion. Let x be the number of women. The proportion becomes 7/4 = 28/x. Cross-multiplying, we get 7x = 112. Solving for x, we find x = 16. Therefore, there are 16 women in the room.

Using the given ratio of apples to bananas (4:9) and the number of apples (36), we can set up a proportion. Let x be the number of bananas. The proportion becomes 4/9 = 36/x. Cross-multiplying, we get 4x = 324. Solving for x, we find x = 81. Therefore, 81 bananas are needed.

Using the given ratio of lemons to limes (5:3) and the number of lemons (20), we can set up a proportion. Let x be the number of limes. The proportion becomes 5/3 = 20/x. Cross-multiplying, we get 5x = 60. Solving for x, we find x = 12. Therefore, 12 limes are needed.

The ratio 5:8 can be expressed as a fraction by putting the first value as the numerator and the second value as the denominator. Therefore, the ratio 5:8 as a fraction is 5/8.

Using the given ratio of apples to oranges (2:7) and the number of apples (18), we can set up a proportion. Let x be the number of oranges. The proportion becomes 2/7 = 18/x. Cross-multiplying, we get 2x = 126. Solving for x, we find x = 63. Therefore, there are 63 oranges in the basket.

Using the given ratio of students to books (6:5) and the number of books (70), we can set up a proportion. Let x be the number of students. The proportion becomes 6/5 = x/70. Cross-multiplying, we get 5x = 420. Solving for x, we find x = 84. Therefore, there are 84 students in the library.

Using the given ratio of boys to girls (2:3) and the number of girls (120), we can set up a proportion. Let x be the number of boys. The proportion becomes 2/3 = x/120. Cross-multiplying, we get 3x = 240. Solving for x, we find x = 80. Therefore, there are 80 boys in the school.

To simplify a ratio, divide both values by their greatest common divisor. The greatest common divisor of 16 and 24 is 8. Dividing both values by 8, we get 2:3. Therefore, the simplified ratio of 16:24 is 2:3.

Let's use the concept of man-hours to solve this problem. The total man-hours required to build the wall is constant.



If 6 workers can build the wall in 4 hours, then the total man-hours is (6 workers * 4 hours) = 24- man-hours.



Now, if you want to build the same wall in 3 hours, you can set up the equation:



{Number of workers} \ {Time (in hours)} = {Total man-hours} 



Let x be the number of workers needed. The equation is:



x* 3 = 24



Now, solve for  x :



x = 24/3



x = 8 



Therefore, you would need 8 workers to build the same wall in 3 hours.

To simplify a ratio, divide both values by their greatest common divisor. The greatest common divisor of 9 and 12 is 3. Dividing both values by 3, we get 3:4. Therefore, the simplified ratio of 9:12 is 3:4.

Given that the ratio of wins to losses is 3:2 and the team has played 30 games, you can use this information to find the number of games they won.



Let x be the number of wins. The ratio of wins to losses is given as 3:2, so you can set up a proportion:



{Number of wins}/{Number of losses} = 3/2



Now, since the team has played 30 games, the total number of games is the sum of wins and losses:



{Number of wins} + {Number of losses} = 30



Substitute the given value for the number of wins in the proportion:



x + 3/2*x = 30



Combine like terms:



5/3* x = 30 



Multiply both sides by 5/3 to solve for x :



x = 3/5* 30

x = 18 



Therefore, they have won 18 games.