Difference and SumPro Problems > Math > Algebra > Equations > Systems of Equations > Word 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?
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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?
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?
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?
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?
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?
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?
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?
The difference between two numbers is twice the smaller number. The smaller number is 10 less than the larger number. Find the smaller number.
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?