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nydus/The First Steps in AlgebraPublic

This textbook introduces the fundamental concepts of algebra, including definitions of units, quantities, and number symbols. It explains the use of letters to represent numbers and outlines the signs for basic mathematical operations.

Page 121 of 227
Table of Contents

X.

  1. The difference of two numbers is 49, and if the greater is divided by the smaller, the quotient is 4 and the remainder 4. Find the numbers.
  1. The difference of two numbers is 91, and if the greater is divided by the smaller, the quotient is 8 and the remainder 7. Find the numbers.
  1. Divide 320 into two parts such that the smaller part is contained in the larger part 11 times, with a remainder of 20.

Exercise 57.

Ex. Eight years ago a boy was one-fourth as old as he will be one year hence. How old is he now?

lint Let x = the number of years old he is now. lint Then x - 8 = the number of years old he was eight years ago, lintand x + 1 = the number of years old he will be one year hence.

x - 8 = 14(x + 1). lint Solving, x = 11.

Therefore the boy is 11 years old.

  1. A son is one-fourth as old as his father. In 24 years he will be one-half as old. Find the age of the son.
  1. B's age is one-sixth of A's age. In 15 years B's age will be one-third of A's age. Find their ages.
  1. The sum of the ages of A and B is 30 years, and 5 years hence B's age will be one-third of A's. Find their ages.
  1. A father
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