HandshakesPro Problems > Math > Algebra > Equations > Systems of Equations > Word Problems
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?
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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?
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?
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?
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?
Five napkins and two forks weigh as much as two plates. Five plates weigh as much as sixteen napkins and four forks. How many napkins weigh as much as a six plates?
The difference between two numbers is twice the smaller number. The smaller number is 10 less than the larger number. Find the smaller number.
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?
The cost of a textbook is directly proportional to the number of math problems it contains, and inversely proportional to the number of authors who wrote the book. A textbook which contains 200 problems, and was written by 3 authors costs $5 less than a textbook which contains 150 problems, and was written by 2 authors. What is the cost of a textbook containing 450 problems, and written by 4 authors?
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?
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?