# A Third of a Fourth

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

## 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

### Next Year

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

### 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?

### 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?

### 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?

### 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?

### 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.

### 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?

### Until New Years Day

The number of seconds until New Years Day (when the ball drops at Midnight) is equal to the number of hours since the last time the ball dropped. Assuming a non-leap-year, what is the current date and time, to the nearest minute?

### Adding It Up

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

### Giant Roller Coaster

An amusement park has an enormous roller coaster with 48 roller coaster cars, each of which was carrying the same number of people. Six of the cars were removed from the coaster, and each of the remaining cars had to carry one extra person. How many people were there on the roller coaster?