Digit problems algebra
Introduction :
Algebra:
Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures.(source : Wikipedia)
Digit problems:
The problems that gives sum of the digits of a number, difference between the digits or multiplication of digits of a number and ask us to find the number. These kinds of problems are called as digit problems. To solve the digit problems we have a good knowledge in place value of numbers.
In this article we are going to see some solved digit problems and practice digit problems in algebra.
Solved digit problems algebra:
Problem 1:
A certain number of 2 digits is three times the sum of its digits and if 45 be added to it, the digits are reversed. Find the number.
Solution:
Given, two digits number is 3 times sum of its digits.
That is, Lets the ten’s digit be x and unit digit be y.
10x + y = 3(x + y) ------------ > 1
When 45 added, the digits are reversed,
10x + y + 45 = 10y + x ------- > 2
From equation 1,
10x + y = 3x + 3y
Subtract 3x and 3y on both sides,
10x + y -3x -3y = 0
7x – 2y = 0 ------------- > 3
From equation 2,
10x + y + 45 = 10y + x
Subtract 10y and x on both sides,
10x + y + 45 – 10y –x = 0
9x – 9y + 45 = 0
9( x – y + 5) = 0
Divide by 9 on both sides,
x – y + 5 = 0
Subtract 5 on both sides,
x – y + 5 - 5 = 5
x – y = -5 ------------------- > 4
From the equation 3 and 4, we can find the x and y value as shown in below,
7x – 2y = 0 ------------- > 3
x – y = -5 ------------------- > 4
Multiply the equation 4 by 2,
2x – 2y = -10 -------------- > 5
Subtract equation 3 and 5,
7x – 2y = 0
(-) 2x – 2y = -10
5x = 10
Divide by 5 on both sides,
x = 2
Substitute x = 2 in equation 4,
x – y = -5
2 – y = -5
Subtract 2 on both sides,
2 – y - 2 = -5 -2
-y = -7
Y =7
Answer: The number is 27
Practice digit problems:
Problems 1:
1.A certain number of 2 digits is 6 times the sum of its digits and if 9 be subtracted to it, the digits are reversed. Find the number.
2.A certain number of 2 digits is 10 times the sum of its digits and if 45 be subtracted to it, the digits are reversed. Find the number.
Answer key:
1. 54
2. 50
Algebra:
Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures.(source : Wikipedia)
Digit problems:
The problems that gives sum of the digits of a number, difference between the digits or multiplication of digits of a number and ask us to find the number. These kinds of problems are called as digit problems. To solve the digit problems we have a good knowledge in place value of numbers.
In this article we are going to see some solved digit problems and practice digit problems in algebra.
Solved digit problems algebra:
Problem 1:
A certain number of 2 digits is three times the sum of its digits and if 45 be added to it, the digits are reversed. Find the number.
Solution:
Given, two digits number is 3 times sum of its digits.
That is, Lets the ten’s digit be x and unit digit be y.
10x + y = 3(x + y) ------------ > 1
When 45 added, the digits are reversed,
10x + y + 45 = 10y + x ------- > 2
From equation 1,
10x + y = 3x + 3y
Subtract 3x and 3y on both sides,
10x + y -3x -3y = 0
7x – 2y = 0 ------------- > 3
From equation 2,
10x + y + 45 = 10y + x
Subtract 10y and x on both sides,
10x + y + 45 – 10y –x = 0
9x – 9y + 45 = 0
9( x – y + 5) = 0
Divide by 9 on both sides,
x – y + 5 = 0
Subtract 5 on both sides,
x – y + 5 - 5 = 5
x – y = -5 ------------------- > 4
From the equation 3 and 4, we can find the x and y value as shown in below,
7x – 2y = 0 ------------- > 3
x – y = -5 ------------------- > 4
Multiply the equation 4 by 2,
2x – 2y = -10 -------------- > 5
Subtract equation 3 and 5,
7x – 2y = 0
(-) 2x – 2y = -10
5x = 10
Divide by 5 on both sides,
x = 2
Substitute x = 2 in equation 4,
x – y = -5
2 – y = -5
Subtract 2 on both sides,
2 – y - 2 = -5 -2
-y = -7
Y =7
Answer: The number is 27
Practice digit problems:
Problems 1:
1.A certain number of 2 digits is 6 times the sum of its digits and if 9 be subtracted to it, the digits are reversed. Find the number.
2.A certain number of 2 digits is 10 times the sum of its digits and if 45 be subtracted to it, the digits are reversed. Find the number.
Answer key:
1. 54
2. 50