# Sum and Difference

Pro Problems > Math > Algebra > Equations > Systems of Equations > Word Problems## 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?

## 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

### Pairs of Consecutives

The sum of two pairs of consecutive integers is 100. the difference between the largest and the smallest of these four integers is 9 less than the average of the four integers.

Find all four integers.

### 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?

### 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.

### 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?

### 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?

### 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?

### Sum of Two Fractions

### Six more than Twice the Smaller

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?

### 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?

### A Sum of Sums

If the sum of an integer and the next consecutive integer is added to the sum of another integer and its next consecutive odd integer, the result is 71.

If the smaller of the two numbers is subtracted from twice the larger, the result is 29. What are the two numbers?