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

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

Answer 2

smaller number = 20 , larger number = 37

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`