Pairs of Consecutives
Pro Problems > Math > Algebra > Equations > Systems of Equations > Word ProblemsPairs of Consecutives
The sum of two pairs of consecutive integers is 100. the difference between the largest and the smallest of these four integers is 9 less than the average of the four integers.
Find all four integers.
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
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?
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?
Humpty 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?
Spiders and ants
In my house there are both ants and spiders. Together there are 240 legs. If there were half as many spiders, and twice as many ants, there would be 336 legs. How many ants do I have in my house?
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?
Napkins, Forks, and Plates
Five napkins and two forks weigh as much as two plates. Five plates weigh as much as sixteen napkins and four forks. How many napkins weigh as much as a six plates?
Sum and Difference
The sum of two numbers is eleven less than four times the smaller number. The difference between the numbers is five more than the smaller number. What is the larger number?
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?
Difference System
The difference between two numbers is twice the smaller number. The smaller number is 10 less than the larger number. Find the smaller number.
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?
Blogs on This Site
Like us on Facebook to get updates about new resources