Answer: 70 and 14
Step-by-step explanation:
Let the bigger number be x and the smaller number be y , then from the first statement
[tex]x + y = 84[/tex]
From the second statement :
four times the smaller number means [tex]4[/tex] x [tex]y[/tex] , which will be [tex]4y[/tex] , so
four times the smaller number is subtracted from the larger number the result is 14 means :
[tex]x - 4y = 14[/tex]
combining the two equations we have :
[tex]x + y = 84[/tex] ........................... equation 1
[tex]x - 4y = 14[/tex] .......................... equation 2
solving the system of linear equation by substitution method , from equation 1 , make x the subject of the formula , that is :
[tex]x = 84 - y[/tex] .......................... equation 3
substitute [tex]x = 84 - y[/tex] into equation 2 , that is
[tex]84 - y - 4y = 14[/tex]
[tex]84 - 5y = 14[/tex]
[tex]84 - 14 = 5y[/tex]
[tex]70 = 5y[/tex]
therefore :
[tex]y = 14[/tex]
substitute [tex]y = 14[/tex] into equation 3 to find the value of x
[tex]x = 84 - y[/tex]
[tex]x = 84 - 14[/tex]
[tex]x = 70[/tex]
check :
[tex]x + y = 84[/tex]
[tex]70 + 14 = 84[/tex]
[tex]x - 4y = 14[/tex]
[tex]70 - 4( 14 )[/tex]
[tex]70 - 56 = 14[/tex]
Therefore : the bigger number is 70 and the smaller number is 14
