Games
Problems
Go Pro!

Handshakes

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

Handshakes

Mr. T wants each of his math students to shake hands with each of his other math students exactly once. He also wants each of his math students to shake Mr. H's hand twice. Mr. T shakes Mr. H's hand once. If there were 78 handshakes in all, how many math students does Mr. T have?

Presentation mode
Problem by Mr. Twitchell

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.
Assign this problem
Click here to assign this problem to your students.

Similar Problems

Chickens and Roosters

My neighbor has both chickens and roosters. He has a total of 31 birds. The number of chickens is ten more than twice the number of roosters. How many chickens does he have?

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?

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?

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?

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?

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.

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?

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?

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.

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?

Triangle Perimeter, Napkins, Forks, and Plates, Sum of Two Fractions, Bag of Candy, Math Textbooks for Sale, Humpty Dumpty, Antique Table Price, Six more than Twice the Smaller, A Sum of Sums, Manny Climbs a Skyscraper

Understanding Coronavirus Spread

A Question and Answer session with Professor Puzzler about the math behind infection spread.

Blogs on This Site

Reviews and book lists - books we love!
The site administrator fields questions from visitors.
Like us on Facebook to get updates about new resources
Home
Pro Membership
About
Privacy