Question

1. the sum of two numbers is 107. their difference is $-45$. what is one of the numbers?

Explanation:

Step1: Define variables for numbers

Let the two numbers be $x$ and $y$.

Step2: Set up system of equations

$$\begin{cases} x + y = 107 \\ x - y = -45 \end{cases}$$

Step3: Add equations to solve for $x$

Add the two equations to eliminate $y$:
$(x + y) + (x - y) = 107 + (-45)$
$2x = 62$
$x = \frac{62}{2} = 31$

Step4: Solve for $y$ (optional)

Substitute $x=31$ into $x + y = 107$:
$31 + y = 107$
$y = 107 - 31 = 76$

Answer:

One of the numbers is $\boldsymbol{31}$ (or $\boldsymbol{76}$)