Question

the sum of two numbers is 60 and the difference is 14. what are the numbers?
larger number:
smaller number:

Explanation:

Step1: Define variables for numbers

Let $x$ = larger number, $y$ = smaller number.

Step2: Set up system of equations

$$\begin{cases} x + y = 60 \\ x - y = 14 \end{cases}$$

Step3: Add equations to solve for x

Add the two equations to eliminate $y$:
$x + y + x - y = 60 + 14$
$2x = 74$
$x = \frac{74}{2} = 37$

Step4: Substitute x to find y

Substitute $x=37$ into $x + y = 60$:
$37 + y = 60$
$y = 60 - 37 = 23$

Answer:

Larger number: 37
Smaller number: 23