algebra

a two digit number is four times the sum of its digits and twice the product of the digit. find the number using elimination method

  1. 👍 0
  2. 👎 0
  3. 👁 134
  1. let the tens digit be x
    let the unit digit be y

    then the number is 10x+y

    10x+y = 4(x+y) ----> 6x - 3y = 0
    6x = 3y
    y = 2x

    10x + y = 2(xy)
    10x - 2xy + y = 0
    10x - 2x(2x) + 2x = 0
    -4x^2 + 12x = 0
    x^2 - 3x= 0
    x(x-3) = 0
    x = 0 or x = 3 , but if x=0 you don't have a 2-digit number

    x = 3, y = 6
    the number is 36

    I used substitution instead of elimination since it was clearly the easiest and most obvious way to do it, because of the simple result of x=2x from the first equation.
    the xy term of the second equation would lead to a more complicated result using elimination.

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. Math

    John chooses a 5-digit positive integer and deletes one of its digits to make a 4-digit number. The sum of this 4-digit number and the original 5-digit number is 52713. What is the sum of the digits of the original 5-digit number?

    asked by Amitabha on March 12, 2016
  2. math

    Form the greatest possible 5-digit number using the clues.All five digits are different. None of the five digit are 1.The digit in the ten thousands place is greater than 7.The sum of all five digit is 18.The greatest digit is

    asked by hawa on September 22, 2017
  3. Math

    A number has three distinct digits. The sum of the digits equals the product of the digits. How many three-digit numbers satisfy this condition?

    asked by Ryan on September 4, 2016
  4. Mathematics

    There is a two-digit number such that the sum of its digit is 6 while the product of the digits is 1/3 of the original number. Find this number. Explain your solution

    asked by Tata on October 23, 2011
  1. Math

    The sum of the digits of a three digit number is 20.The middle digit is equal to one fourth the sum of the other two. If the order of the digits is reversed the number increases by 198. Find original number

    asked by Rohan on December 3, 2017
  2. Math

    If a positive two-digit integer is divided by the sum of its digits, the quotient is 2 with a remainder of 2. If the same two-digit integer is multiplied by the sum of its digits, the product is 112. What is the two-digit integer?

    asked by Kinnari on January 9, 2011
  3. math

    While adding ten two-digit numbers the digits of one of the numbers were interchanged. As a result the sum of all the ten numbers increased by a value which was four less than that number. Three times the sum of the digits of the

    asked by Suzanne on November 13, 2014
  4. 5th grade math

    i am a number greater than 40,000 and less than 60,000 my ones digit and tens digits are the same. my ten thousands digit is 1 less tha 3 times the sum of my ones digit and tens digit my thousands digit is half my hundred digit,

    asked by edgar on August 22, 2010
  1. MATH

    A number has three distinct digits. The sum of the digits equals the product of the digits. How many three-digit numbers satisfy this condition?

    asked by Jhon on September 3, 2016
  2. Maths

    A two digit number is formed by either substracting 17 from nine times the sum of the digits or by adding 21 to 13 times the difference of the digits .find the number

    asked by Anu on June 29, 2013
  3. maths

    Find the sum of all 3-digit positive numbers N that satisfy the condition that the digit sum of N is 3 times the digit sum of N+3. Details and assumptions The digit sum of a number is the sum of all its digits. For example, 1123

    asked by rohit on March 21, 2013
  4. MATH

    I am a 3 digit number dividible by 3. My tens digit is 3 times as great as my hundreds digit, and the sum of my digits is 15. If you reverse my digits, I am divisible by 6, as well as by 3. What number am I?

    asked by Tina on November 18, 2008

You can view more similar questions or ask a new question.