Lesson OVERVIEW of lessons for word problems on finding numbers

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OVERVIEW of lessons for word problems on finding numbers


My lessons in this site for word problems on finding numbers are

    - Simple and simplest word problems on finding numbers solved by different methods
    - Find the number using a single linear equation
    - Find the number using quadratic equation
    - Find the numbers using system of equations
    - Digit problems - Find the number using system of equations
    - Entertainment problems on finding numbers

List of lessons with short annotations


Simple and simplest word problems on finding numbers solved by different methods

        Problem 1.  From a certain number,  '3'  is subtracted and the result is divided by  2.
                           The final answer is  5.  Find the number.

        Problem 2.  The sum of two numbers is  21.  Five times the first number added to  2  times the second number is  66.
                           Find the numbers.

        Problem 3.  You have  2  positive numbers.  One number is one-fifth of the other number.
                           The difference between the two numbers is  284.  Find the numbers.


Find the number using a single linear equation

        Problem 1.  Twice a number is added to the number,  giving  90.  Find the number.

        Problem 2.  When  6  is subtracted from a number,  the result is seven times the number.  Find the the number.

        Problem 3.  Four times a number is equal to twelve more than the number.  Find the number.

        Problem 4.  Twice a number is twenty less than the product of seven and the number.  Find the number.

        Problem 5.  One number is  17  less than another and their sum is  125.  Find the numbers.

        Problem 6.  The sum of the digits of a two digit number is  11.  The new number obtained when the digits are reversed
                           is  7  more than twice the original number.  Find the original number.

        Problem 7.  One number is bigger than another by  406.  If the bigger number is divided by the smaller one,  you’ll get the quotient  3  and remainder  66.
                           Find the numbers.

        Problem 8.  The unit digit of a two digit number is  1  less than the tens digit.
                           If the number is increased by  8  and then divided by the sum of the digits,  the result is  8.
                           Find the number.


Find the number using quadratic equation

        Problem 1.  Find two integers with a product of  -40  and a sum of  -3.

        Problem 2.  Two positive integers differ by  6.  Their product is  616.  Find the integers.

        Problem 3.  The difference of two positive numbers is six.  Their product is  223  less than the sum of their squares.
                           What are the two numbers?

        Problem 4.  The sum of a number and its reciprocal is  10/3.  What is the number?

        Problem 5.  One positive number is  10  less than another positive number.  If the reciprocal of the smaller number is added
                           to three times the reciprocal of the larger number,  the sum is  1/4.  Find the two numbers.

        Problem 6.  The product of two consecutive odd integers is  323.  Find the integers.


Find the numbers using system of equations

        Problem 1.  If the larger of two numbers is divided by the smaller,  the quotient is  7  and the remainder is  19.
                           But if  3  times the greater is divided by twice the smaller,  the quotient is  11  and the remainder is  19.
                           What are the numbers?

        Problem 2.  Three times the smaller of two numbers plus  2  times the larger number is  27.
                           Four times the smaller number minus  2  times the larger number is  -6.  Find the numbers.

        Problem 3.  The tens digit of a two digit number is  2  less than the units digit.
                           The difference between the squares of the digits is  32.  What is the number ?

        Problem 4.  The sum of three numbers is  14.  The sum of twice the first number,  4  times the second number,  and  5  times the third number is  62.
                           The difference between  4  times the first number and the second number is negative  1.  Find the three numbers.

        Problem 5.  The sum of three numbers is  1.  If the second number is subtracted from the sum of the first and third numbers,  the result is  -1.
                           If the third number is subtracted from the sum of the first and second numbers,  the result is  -9.  Find the three numbers.

        Problem 6.  The sum of three numbers is  8.  The first number minus the second plus the third is  4.
                           The first minus the third is  2  more than the second.  Find the numbers.

        Problem 7.  The difference between two positive integers is  5  and the difference between their reciprocals is   5%2F24.   Find the integers.


Digit problems - Find the number using system of equations

        Problem 1.  A two-digit number is  6  times the units digit.  Find the number if the sum of its digit is  6.

        Problem 2.  A two-digit number is  2  more than  8  times the sum of its digits.
                           Find the number if its tens digit is  6  more than its unit digit.

        Problem 3.  The sum of the digits of a two-digit number is 11.
                           If the digits are reversed, the new number is 45 less than the original number.
                           Find the number.

        Problem 4.  A two digit number is such that its tens digit is greater than its unit digit by  5.
                           If the number is  14  less than  3  times the product of its digits,  find the number


Entertainment problems on finding numbers

        Problem 1.  Find a two-digit positive even integer number less than  90  with the sum of digits  15.

        Problem 2.  The product of two consecutive odd integers is  323.  Find the integers

        Problem 3.  Find two numbers whose sum is  1  and product is  4/25.

        Problem 4.  A five digit number is the fourth power of an integer.  The sum of the first,  third,  and fifth digits
                           equals the sum of the second and fourth digits.  What is the number ?


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