Question

The sum of two numbers is thirteen. Using x to represent the smaller of the two numbers, translate "the sum of two more than the larger number and twice the smaller number" into a variable expression. Then simplify.

Answer 1

Let x be the smaller and y be the largest number.

Since $x+y=13$, we deduce $y=13-x$

Now, for the translation: "two more than the larger number" is $y+2$, while "twice the smaller" is $2x$

Their sum is

$y+2+2x$

And since we know that $y=13-x$, we have

$y+2+2x = 13-x+2+2x = 15+x$