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From: porkchop@invalid.foo (Mike Sanders)
Newsgroups: comp.lang.awk
Subject: 100 Random Single Variable Linear Equations
Date: Fri, 6 Dec 2024 03:46:32 -0000 (UTC)
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Beware wordwrap...

# algebra.awk: 2024 - Michael Sanders
#
# usage: awk -f algebra.awk > solve.txt
#
# outputs 100 random single variable linear equations in the form: ax+b=c
#
# where...
#
# a, b, & c are constants (numbers)
# x is the variable
#
# example output...
#
# 001. 18x * 20 = 27
# 002. 1x * 16 = 31
# 003. 10x / 8 = 16
#
# solving for x...
#
# 1. solving for x means finding the value of x that makes the equation true.
#
# 2. how to do it:
#   - look at the equation & see if x is combined with numbers or other terms.
#   - use inverse operations to "cancel out" numbers or terms that are with x.
#
#   for example:
#   - if x is multiplied by a number, divide both sides of the equation by that number.
#   - if x is divided by a number, multiply both sides of the equation by that number.
#   - if x is added to a number, subtract that number from both sides.
#   - if x has a number subtracted from it, add that number to both sides.
#
# 3. example, solve for x in the equation: 2x + 5 = 11
#
#   - step 1: subtract 5 from both sides:
#     to remove the +5 from the left side, subtract 5 from both sides:
#     (2x + 5) - 5 = 11 - 5
#
#     simplify:
#     2x = 6
#
#   - step 2: divide both sides by 2:
#     to remove the 2 multiplying x, divide both sides by 2:
#     (2x) / 2 = 6 / 2
#
#    simplify:
#    x = 3
#
# 4. final answer: x = 3
#
# 5. why it works:
#    you perform the same operation on both sides of the equation,
#    keeping it balanced, until x is by itself on one side.
#
# further reading: https://en.wikipedia.org/wiki/Algebra

BEGIN {
    srand() # seed random number generator

    for (q = 1; q <= 100; q++) {
        # generate random coefficients & constant
        a = int(rand() * 20) + 1 # random value for 'a' (1 to 20)
        b = int(rand() * 20) + 1 # random value for 'b' (1 to 20)
        c = int(rand() * 50) + 1 # random value for 'c' (1 to 50)

        opc = (rand() < 0.5 ? "*" : "/")      # random operator
        lhs = sprintf("%dx %s %d", a, opc, b) # left-hand side
        rhs = c                               # right-hand side

        # format equation number with zero-padding
        equation = sprintf("%03d", q)

        # blank lines after equations
        bla = sprintf("\n\n\n\n\n\n\n\n\n")

        # print formated equation
        printf("%s. %s = %d%s", equation, lhs, rhs, bla)

    }
}

# eof

-- 
:wq
Mike Sanders