# Antique Table Price

Pro Problems > Math > Algebra > Equations > Systems of Equations > Word Problems## Antique Table Price

The price of an antique table varies directly with age of the antique (in years) and with the surface area (in square feet). The price varies inversely with the number of scratches on the surface. A table which is 120 years old, is 3 feet x 8 feet , and has n scratches on the surface, costs $4,320. A table which is 140 years old, is 4 feet x 8 feet, and has n - 1 scratches on the surface, costs $7,680. If a table 150 years old, which is 4 feet x 6 feet , costs $10,800, how many scratches are on the surface?

## 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

### Henry's Books

Henry has five books. The third book has 100 fewer pages than the first and second books combined. The fourth book has 50 pages more than twice the number of pages in the first book. The last book has 150 fewer pages than three times the second book. In all, his books have 748 pages. Together, his first and second books have 216 pages. How many pages does his largest book have?

### 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?

### Coffee and Donuts

I went to a café and purchased a cup of coffee, and two donuts. I spent $2.66. Then I purchased two cups of coffee and one donuts for $3.10. How much does a cup of coffee cost?

### Manny Climbs a Skyscraper

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 n^{th} 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 k^{th} 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?

### Sum and Difference

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?

### 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?

### 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.

### Sum of Two Fractions

### 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?

### Triangle Perimeter

The shortest side of a triangle has length 16 inches. The perimeter of the triangle is nineteen less than three times the longest side.The remaining side is eight inches shorter than the longest side. What are the side lengths of the triangle?