Square of a Sum
Pro Problems > Math > Algebra > Equations > Word Problems > LinearSquare of a Sum
The sum of the squares of two positive numbers is 96 less than the square of the sum of the two numbers. If one number is two more than the other, what are the two numbers?
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
Yards and Feet
The height of a building measured in feet is 196 more than its height measured in yards. What is the height of the building in feet?
Stair climber
Nathan started at the bottom of the stairs and climbed n steps. After that he went down n - 4 steps, and was then 15 steps from the top of the stairs. How many steps are there?
Find the Number
The sum of a number and twice that number is 20% more than the result would have been if the number had been increased by 12 and then doubled. What is the number?
A Third of a Fourth
Half of a third of a number is decreased by six, and a third of a fourth of the result is increased by ten. One fifth of the result is 17. What is the original number?
White Board Markers
I have a problem with dry erase markers disappearing from my classroom. A third of my markers were stolen by a student, and then one of my co-workers "borrowed" four markers. After that I realized that half of the remaining markers didn't work, so I threw them away.
In the end, I just had two markers left.
How many did I start with?
Moving Christmas
Hermie doesn't want to celebrate Christmas on December 25th, so he suggested moving it to a date n days later. Rudolph protested that then Christmas wouldn't happen as often.
Frosty then suggested that the date could be moved n days in the other direction. If Frosty's suggestion was followed, on what day would Christmas fall?
Snake in the Grass
Two snakes started out the same length. The first snake grew five inches, and the second grew by half its own length. If the first snake is now two inches shorter than the second snake, what was the original length of the two snakes?
Single variable equation
A number, plus 5 more than that number, plus twice the sum of 5 and that number, is 43. What is the number?
Adding It Up
The sum of a number and five more than that number is 47. What is the number?
Three Numbers
I have a sheet of paper with three integers written on it. If I add them together, I have a sum of 38.
Two of the numbers differ by one. One of the three numbers is 11.
What is the largest possible integer that could be written on the paper?
Blogs on This Site
Like us on Facebook to get updates about new resources