# A Sum of Sums

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

## 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

### Spiders and ants

In my house there are both ants and spiders. Together there are 240 legs. If there were half as many spiders, and twice as many ants, there would be 336 legs. How many ants do I have in my house?

### 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?

### Humpty Dumpty

The reason the king's horses and the king's men couldn't put Humpty Dumpty back together again is that the king's horses were no help whatsoever. In fact, the king's horses (who are not very handy) accidentally break pieces instead of putting them together.

One king's man can put together two pieces every 5 seconds.

One king's horse can break a piece in two every 2 seconds.

There are twenty more men than horses.

If there had been six fewer men, and horses broke pieces at a rate of one every three seconds, they could have done the job.

If the number of men and the number of horses are both prime numbers, how many men and horses are there?

### 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?

### 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?

### 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.

### Sum of Two Fractions

### 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?