The sum of two numbers is 13 more than twice the first number the difference is 14 less than the second number find each of the numbers

Answer 1

One of the keys to this question is to write out the problem in terms of an equation.

Let's start with the first part of the problem statement: The sum of two numbers (we'll call these X and Y for now) is 13 more than twice the first number (what we call X).

In equation form: X + Y = 13 + 2(X) (Equation 1)

Second part: The difference (of X and Y) is 14 less than the second number (Y).

In equation form: X - Y = Y - 14 (Equation 2)

Now, we can use the two equations above to solve for X and Y, our two numbers.

X + Y = 13 + 2X (Equation 1)

-X -X

Y = 13 + X (Equation 1 Rewritten)

Sub in the rewritten Equation 1 above into Equation 2:

X - Y = Y - 14 (Equation 2)

X - (13 + X) = (13 + X) - 14 (Equation 2 with Y substituted in using what we found from Equation 1)

X - 13 - X = 13 + X - 14 (Distribute the negative)

-13 = 13 + X - 14

-13 = -1 + X

X = -12

Substitute the value of X into Equation 1 to find Y:

Y = 13 + X

Y = 13 + (-12)

Y = 1

Answer: Our numbers are -12 and 1.

Hope this helps and let me know if anything is confusing!