Mathematics Puzzles

To find the total number of animals, we add the number of sheep, cows, and pigs: 12 + 6 + 8 = 26.

To find the time at which the two trains meet, we need to calculate the total time it takes for them to travel the distance between New York City and Chicago. The first train travels for 1 hour before the second train leaves, so it covers 60 miles. The second train travels for 2 hours before they meet, so it covers 140 miles. The total distance covered by both trains is 900 miles, so the time they meet is 3 hours after the second train leaves, which is 3:00 PM.

In the given code, each letter is represented by a number that corresponds to its position in the alphabet. For example, 'C' is the 3rd letter in the alphabet, so it is represented by '3'. Similarly, 'A' is the 1st letter, so it is represented by '1', and 'T' is the 20th letter, so it is represented by '2'. Using this pattern, we can decode 'RAT' as follows: 'R' is the 18th letter, so it is represented by '2', 'A' is the 1st letter, so it is represented by '1', and 'T' is the 20th letter, so it is represented by '3'. Therefore, the code for 'RAT' is '231'.

To calculate the total amount the customer pays, we multiply the price of each item by the quantity purchased and then add the results: (3 apples x $1 each) + (2 oranges x $0.50 each) + (1 banana x $0.25 each) = $3 + $1 + $0.25 = $4.25. Therefore, the customer pays $4.50 in total.

To find the area of the path, we need to calculate the area of the new garden (including the path) and subtract the area of the original garden. The new garden has a length of 12 + 2 + 2 = 16 feet and a width of 8 + 2 + 2 = 12 feet. Therefore, the area of the new garden is 16 x 12 = 192 square feet. The area of the original garden is 12 x 8 = 96 square feet. Subtracting the area of the original garden from the area of the new garden, we get 192 - 96 = 96 square feet. However, since the path surrounds the garden, we need to divide this value by 2 to get the area of the path, which is 96 / 2 = 64 square feet.

To find the average speed for the round trip, we need to calculate the total distance traveled and the total time taken. The total distance is 200 miles (from City A to City B) + 200 miles (from City B to City A) = 400 miles. The time taken for the first trip is 200 miles / 50 miles per hour = 4 hours. The time taken for the return trip is 200 miles / 60 miles per hour = 3.33 hours. The total time taken for the round trip is 4 hours + 3.33 hours = 7.33 hours. Therefore, the average speed for the round trip is 400 miles / 7.33 hours = 54.54 miles per hour, which is approximately 56 miles per hour.

To find the number of employees who remain, we need to calculate the number of employees who leave and subtract that from the total number of employees. The number of male employees who leave is 20% of 60, which is 0.20 x 60 = 12. The number of female employees who leave is 30% of 40, which is 0.30 x 40 = 12. Therefore, the total number of employees who leave is 12 + 12 = 24. Subtracting this from the total number of employees, we get 100 - 24 = 76. However, since the question asks for the number of employees who remain, we need to add back the number of employees who did not leave. The number of male employees who remain is 60 - 12 = 48, and the number of female employees who remain is 40 - 12 = 28. Therefore, the total number of employees who remain is 48 + 28 = 64.

The perimeter of a rectangle is the sum of the lengths of all four sides. In this case, the perimeter is 40 feet, so we have 2(12 feet + 8 feet) = 40 feet. Simplifying this equation, we get 20 feet + 16 feet = 40 feet. Subtracting 20 feet from both sides, we get 16 feet = 24 feet. Therefore, the area of the room is 12 feet x 8 feet = 96 square feet.

To find the sale price of the shirt, we need to calculate the amount of the discount and then subtract that from the original price. The amount of the discount is 20% of $20, which is 0.20 x $20 = $4. Subtracting this from the original price, we get $20 - $4 = $16. Therefore, the sale price of the shirt is $16.

To find the time at which the two trains meet, we need to calculate the total time it takes for them to travel the distance between New York City and Chicago. The first train travels for 1 hour before the second train leaves, so it covers 70 miles. The second train travels for x hours before they meet, so it covers 80x miles. The total distance covered by both trains is 900 miles, so we have 70 + 80x = 900. Solving for x, we get x = 10. Therefore, the two trains meet 10 hours after the second train leaves, which is 11:00 AM + 10 hours = 2:00 PM.

To find the area of the path, we need to calculate the area of the new garden (including the path) and subtract the area of the original garden. The new garden has a length of 15 + 2 + 2 = 19 feet and a width of 10 + 2 + 2 = 14 feet. Therefore, the area of the new garden is 19 x 14 = 266 square feet. The area of the original garden is 15 x 10 = 150 square feet. Subtracting the area of the original garden from the area of the new garden, we get 266 - 150 = 116 square feet. However, since the path surrounds the garden, we need to divide this value by 2 to get the area of the path, which is 116 / 2 = 60 square feet.

To find the number of employees who remain, we need to calculate the number of employees who leave and subtract that from the total number of employees. The number of male employees who leave is 25% of 60, which is 0.25 x 60 = 15. The number of female employees who leave is 35% of 40, which is 0.35 x 40 = 14. Therefore, the total number of employees who leave is 15 + 14 = 29. Subtracting this from the total number of employees, we get 120 - 29 = 91. However, since the question asks for the number of employees who remain, we need to add back the number of employees who did not leave. The number of male employees who remain is 60 - 15 = 45, and the number of female employees who remain is 40 - 14 = 26. Therefore, the total number of employees who remain is 45 + 26 = 84.

The perimeter of a rectangle is the sum of the lengths of all four sides. In this case, the perimeter is 60 feet, so we have 2(18 feet + 12 feet) = 60 feet. Simplifying this equation, we get 30 feet + 24 feet = 60 feet. Subtracting 30 feet from both sides, we get 24 feet = 30 feet. Therefore, the area of the room is 18 feet x 12 feet = 216 square feet.

To find the sale price of the shirt, we need to calculate the amount of the discount and then subtract that from the original price. The amount of the discount is 30% of $30, which is 0.30 x $30 = $9. Subtracting this from the original price, we get $30 - $9 = $21. Therefore, the sale price of the shirt is $21.