Question

The sum of two numbers is 67 one number is 14 less than twice the other number find the two numbers define your variables

Answer 1

-We need to start by first declaring variables to our numbers. We will use 'a' for the first number and 'b' for the second number.

-These are what the equations would look like because of what was said in the description.


a + b = 67

a = 2b - 14


now we can substitute 'a' into the first equation since it is given to us.

(2b - 14) + b = 67

-Now we can simplify until we get 'b' alone

3b - 14 = 67

3b = 81

b = 27

-Now, substitute 'b' into the first equation and simplify until 'a' is alone.

a + 27 = 67

a = 40

-To check this we can substitute our answers into the second equation since we already know it works on the first one.

(40) = 2(27) - 14

40 = 54 - 14

40 = 40

-So in conclusion your answers would be:

First number (a) = 40

Second number (b) = 27

Answer 2

If the other number is x, then the first can be expressed as 2x-14. Then the sum of the numbers is
x + 2x - 14 = 67
3x - 14 = 67
3x = 81
x = 27
2x - 14 = 40
The numbers are 27 and 40.