Question

the sum of two numbers is 57. If the larger number is three less than twice the smaller number find both numbers

Answer 1

Answer:

smaller number = 20 , larger number = 37

Step-by-step explanation:

Let the smaller number be x  and the larger number be.

Therefore : the sum of two numbers is 57 means

x + y = 57 ....................... equation 1

the larger number is three less than twice the smaller number means :

y + 3 = 2x ............................ equation 2

Solving the system of linear equation by substitution method , make x the subject of the formula in equation 1 , that is

$x = 57 - y$ ............................. equation 3

substitute equation 3 into equation 2 , equation 2 becomes

$y + 3 = 2(57 - y )$

$y + 3 = 114 - 2y$

collect the like terms

$y + 2y = 114 - 3$

$3y = 111$

$y = 37$

substitute $y = 37$ into equation 3 to find the value of x

$x = 57 - y$

$x = 57 - 37$

$x = 20$

Answer 2

Answer:

Step-by-step explanation:

x = larger number, y = smaller number

x + y = 57

x = 2y - 3

2y - 3 + y = 57

3y - 3 = 57

3y = 57 + 3

3y = 60

y = 60/3

y = 20 <=== the smaller number

x = 2y - 3

x = 2(20) - 3

x = 40 - 3

x = 37 <=== the larger number