Humpty Dumpty
Pro Problems > Math > Algebra > Equations > Systems of Equations > Word ProblemsHumpty Dumpty
The reason the king's horses and the king's men couldn't put Humpty Dumpty back together again is that the king's horses were no help whatsoever. In fact, the king's horses (who are not very handy) accidentally break pieces instead of putting them together.
One king's man can put together two pieces every 5 seconds.
One king's horse can break a piece in two every 2 seconds.
There are twenty more men than horses.
If there had been six fewer men, and horses broke pieces at a rate of one every three seconds, they could have done the job.
If the number of men and the number of horses are both prime numbers, how many men and horses are there?
Solution
In order to make it feasible for teachers to use these problems in their classwork, no solutions are publicly visible, so students cannot simply look up the answers. If you would like to view the solutions to these problems, you must have a Virtual Classroom subscription.
Similar Problems
Difference and Sum
Two numbers add to twenty-seven more than the opposite of the smaller number. The numbers differ by three. What is the larger number?
X to Y to Z
Y is three more than twice the square of X, and Z is the square of Y, decreased by twice Y. If four times the square of X is multiplied by 2 more than the square of X, and the result is subtracted from Z, what will the final result be?
Sum of Two Fractions
Triangle Perimeter
The shortest side of a triangle has length 16 inches. The perimeter of the triangle is nineteen less than three times the longest side.The remaining side is eight inches shorter than the longest side. What are the side lengths of the triangle?
A Sum of Sums
If the sum of an integer and the next consecutive integer is added to the sum of another integer and its next consecutive odd integer, the result is 71.
If the smaller of the two numbers is subtracted from twice the larger, the result is 29. What are the two numbers?
Three Digits by Sums
I am a three digit number. The sum of my first two digits is 15, and the sum of my last two digits is 8. The sum of my first and last digits is 7. What number am I?
Six more than Twice the Smaller
The sum of two numbers is six more than twice the smaller number, and if the larger number is multiplied by three, the result is ten less than seven times the smaller number. What is the larger number?
Antique Table Price
The price of an antique table varies directly with age of the antique (in years) and with the surface area (in square feet). The price varies inversely with the number of scratches on the surface. A table which is 120 years old, is 3 feet x 8 feet , and has n scratches on the surface, costs $4,320. A table which is 140 years old, is 4 feet x 8 feet, and has n - 1 scratches on the surface, costs $7,680. If a table 150 years old, which is 4 feet x 6 feet , costs $10,800, how many scratches are on the surface?
Math Textbooks for Sale
The cost of a textbook is directly proportional to the number of math problems it contains, and inversely proportional to the number of authors who wrote the book. A textbook which contains 200 problems, and was written by 3 authors costs $5 less than a textbook which contains 150 problems, and was written by 2 authors. What is the cost of a textbook containing 450 problems, and written by 4 authors?
Chickens and Roosters
My neighbor has both chickens and roosters. He has a total of 31 birds. The number of chickens is ten more than twice the number of roosters. How many chickens does he have?
Understanding Coronavirus Spread
Blogs on This Site
Like us on Facebook to get updates about new resources