The sum of two numbers is 22. Their difference is 4. What is the greater of the two numbers?
Let the two numbers be $x$ and $y$, where $x>y$. We wish to find $x$. The problem can be rewritten as the system of equations: \begin{align*}
x+y&= 22\\
x-y&= 4
\end{align*} Adding these gives: \begin{align*}
2x &= 26\\
x &=\boxed{13}.
\end{align*}
13
Level 1
Algebra
Problem: The sum of two numbers is 22. Their difference is 4. What is the greater of the two numbers?
Solution:<|START_OF_LATENT|><|PRIOR_PREFIX|>To find the two numbers, let the first number be x and the second number be y. The problem states two equations based on the information given: 

1. The sum of the two numbers: x + y = 22
2. The difference of the two numbers: x - y = 4

To solve these equations, we can use the method of substitution or elimination. Here, we will use elimination. 

First, we can add the two equations together to eliminate y:

(x + y) + (x - y) = 22 + 4
2x = 26

Now, divide both sides by 2 to solve for x:

x = 13

Next, we substitute the value of x back into one of the original equations to find y. We can use the first equation:

13 + y = 22

Now, subtract 13 from both sides:

y = 22 - 13
y = 9

Now we have both numbers: x = 13 and y = 9. The problem asks for the greater of the two numbers. Since 13 is greater than 9, the final answer is 13.<|END_OF_LATENT|> The final answer is $13$.