Games
Problems
Go Pro!

Pairs of Consecutives

Pro Problems > Math > Algebra > Equations > Systems of Equations > Word Problems
 

Pairs 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.

Presentation mode
Problem by madelynK

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.
Assign this problem
Click here to assign this problem to your students.

Similar Problems

Henry's Books

Henry has five books. The third book has 100 fewer pages than the first and second books combined. The fourth book has 50 pages more than twice the number of pages in the first book. The last book has 150 fewer pages than three times the second book. In all, his books have 748 pages.  Together, his first and second books have 216 pages. How many pages does his largest book have?

Handshakes

Mr. T wants each of his math students to shake hands with each of his other math students exactly once. He also wants each of his math students to shake Mr. H's hand twice. Mr. T shakes Mr. H's hand once. If there were 78 handshakes in all, how many math students does Mr. T have?

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?

Humpty Dumpty

Humpty Dumpty sat on a wall,
Humpty Dumpty had a great fall;
All the king's horses and all the king's men
Couldn't put Humpty together again.

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?

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?

Manny Climbs a Skyscraper

Manny is climbing to the top of skyscraper, starting from the ground floor (Floor #1). There are 12 steps between each floor. When he reaches the landing for the nth floor, the number of floors he has left to climb is equal to a quarter of the number of steps he's already climbed. When he reaches the landing for the kth floor, the number of floors he has left to climb is equal to one sixth the number of steps he's already climbed.

When Manny has climbed halfway to the top of the skyscraper, the number of steps he has climbed is a three digit number, with the digits in descending order from left to right.

If the skyscraper has at least 40 floors, and no more than 110 floors, how many stairs does Manny climb in all?

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?

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.

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?

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 of Two Fractions, Bag of Candy, Chickens and Roosters, Coffee and Donuts, Difference and Sum, X to Y to Z, Six more than Twice the Smaller, Sum and Difference, Antique Table Price, Spiders and ants

Featured Resources on This Site

Create Christmas ornaments and more
Print fun mazes in many different shapes

Blogs on This Site

Reviews and book lists - books we love!
The site administrator fields questions from visitors.
Like us on Facebook to get updates about new resources
Home
Pro Membership
About
Privacy