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
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?
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?
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
Bag of Candy
Three children share a box of candy between them. Linda gets three times as many peppermints as Shannon, who gets 5 more licorice sticks than Yvette. Yvette gets three times as many licorice sticks as Linda, and half as many peppermints as Linda and Shannon combined. If Shannon got two more licorice sticks than peppermints, and there are 98 candies in all, how many peppermints were there?
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?
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.
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?
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?
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?
Blogs on This Site
Like us on Facebook to get updates about new resources