# Square of a Sum

Pro Problems > Math > Algebra > Equations > Word Problems > Linear## Square 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

### 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?

### Finding X

Two more than twice the sum of x and five is equal to twelve less than three times the sum of x and two.

### 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?

### Melting Snow

The day after a snowstorm, 25% of the snow that fell melted. Then there was another snowstorm in which twice as much snow fell as in the first storm. Then 25% of the total remaining snow on the ground melted, leaving 33 inches. How much snow fell in the first storm?

### Three Numbers

I'm thinking of three numbers. The second number is fourteen more than the first number, and the third number is twice the second number. If the first number is subtracted from the third, the result is 44. What is the third number?

### 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?

### 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?

### Adding It Up

The sum of a number and five more than that number is 47. What is the number?

### Next Year

Next year, Martha will be three times as old as she was 17 years ago. How old is Martha now?

### 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?