Question

The sum of two numbers is 46. the smaller number is 10 less than the larger number. what are the numbers?

Answer 1

x=18,y=28

Explanation:

So, we have the following system of equations:

x+y=46 Eq 1

y=x+10 Eq 2

Substituting

[Eq.2]in [Eq.1:

x+(x+10)=46

Simplifying

2x=36

Solving for x:

x=
`(36)/(2)`=18

Replacing x=18 in [Eq.2]:

y=(18)+10

Therefore, the two numbers are: x=18,y=28

Answer 2

larger number = 28, smaller number = 18

Explanation:

larger number = x

smaller number = x - 10

x + x - 10 = 46

add both x's to get 2x

2x - 10 = 46

add 10 to both sides

2x = 56

divide both sides by 2

x = 28 (larger number)

larger number = 28

smaller number = (28) - 10 = 18