Question

The sum of two numbers is 84. If four times the smaller number is subtracted from the larger number the result is 14. Find the two numbers

Answer 1

Answer:

y=14

Step-by-step explanation:

x + y = 84

-1(x - 4y = 14)

-x + 4y = -14

x + y = 84

-x + 4y = -14

5y = 70

divide by 5

y = 14

Answer 2

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

$x + y = 84$

From the second statement :

four times the smaller number means $4$ x $y$ , which will be $4y$ , so

four times the smaller number is subtracted from the larger number the result is 14 means :

$x - 4y = 14$

combining the two equations we have :

$x + y = 84$ ........................... equation 1

$x - 4y = 14$ .......................... equation 2

solving the system of linear equation by substitution method , from equation 1 , make x the subject of the formula , that is :

$x = 84 - y$ .......................... equation 3

substitute $x = 84 - y$ into equation 2 , that is

$84 - y - 4y = 14$

$84 - 5y = 14$

$84 - 14 = 5y$

$70 = 5y$

therefore :

$y = 14$

substitute $y = 14$ into equation 3 to find the value of x

$x = 84 - y$

$x = 84 - 14$

$x = 70$

check :

$x + y = 84$

$70 + 14 = 84$

$x - 4y = 14$

$70 - 4( 14 )$

$70 - 56 = 14$

Therefore : the bigger number is 70 and the smaller number is 14