Solving Number Problems Involving System of Equations in Two Variables
Solving Number Problems Involving System of Equations In Two Variables
One of the most common applications of equations are number problems. This hub presents five number problems involving system of equations in two variables.
Problem Number One :
The sum of two numbers is 70. The smaller number increased by twenty equals the bigger number. What are these two numbers ?
Solution :
Let X = smaller number
Let Y = bigger number
Equation one : X + Y = 70
Equation Two: X + 20 = Y
Substitute equation 2 in equation one :
X + X + 20 = 70
2X + 20 = 70
2X = 70 – 20
2X = 50
(1/2) 2X = 50 (1/2)
X = 25
Y = 25 + 20 = 45
The two numbers are 25 and 45
Problem Number Two :
The sum of two numbers is 100. The bigger number is four times as large as the smaller number. Find the two numbers.
Solution :
Let X = smaller number
Let Y = bigger number
Equation one : X + Y = 100
Equation two: Y = 4X
Substituting Equation two in equation one :
X + 4X = 100
5X = 100
(1/5) 5X = 100 (1/5)
X = 20
Y = 4(20) = 80
The two numbers are 20 and 80
Problem Number Three :
A number is thrice as large as the other number. The smaller number is 25 less than half the larger number. Find these numbers.
Solution:
Let X = smaller number
Let Y = bigger number
Equation one : Y = 3X
Equation Two : X = y/2 – 25
Substituting equation one in equation two :
X = 3X/2 - 25
2 ( X = 3X/2 - 25) 2
2X = 3X - 50
2X – 3X = -50
-1 ( -X = - 50 )
X = 50
Y = 3 (50) = 150
The two numbers are 50 and 150
Sample Problem Number Four :
A certain number is ten times as large as the other number. This number is 50 greater than eight times the smaller number. Find these two numbers.
Solution :
Let X = smaller number
Let Y = the larger number
Equation one: Y = 10X
Equation Two : Y = 8X + 50
Substituting Equation one in equation two :
10X = 8X + 50
10X – 8X = 50
2X + 50
(1/2) 2X = 50 (1/2)
X = 25
Y = 10 (25) = 250
The two numbers are 25 and 250
Sample Problem Number Five :
The sum of two numbers is 70. The smaller number increased by 90 is equal to thrice the bigger number. Find these two numbers.
Solution :
Let X = smaller number
Let Y = bigger number
Equation one : X + Y = 70
Equation Two : X + 90 = 3Y
We will solve this using the elimination method by subtraction
X + Y = 70
(-) X - (+) 3Y =(+) -90
(1/4) 4Y = 160 (1/4)
Y = 40
X = 70 – 40 = 30
The two numbers we are looking for are 30 and 40.
