Question

the sum of two numbers is 52 and the difference is 20. what are the numbers?
larger number:
smaller number:

Explanation:

Step1: Define variables for numbers

Let the larger number be $x$, smaller be $y$.

Step2: Set up system of equations

$$\begin{cases} x + y = 52 \\ x - y = 20 \end{cases}$$

Step3: Add equations to solve for $x$

Add the two equations: $(x + y) + (x - y) = 52 + 20$
Simplify: $2x = 72$ → $x = \frac{72}{2} = 36$

Step4: Substitute $x$ to find $y$

Substitute $x=36$ into $x + y = 52$: $36 + y = 52$
Solve for $y$: $y = 52 - 36 = 16$

Answer:

Larger number: 36
Smaller number: 16