One number is 4 more than 5 times another. their sum is 34. find the two numbers.

The first answer is correct, but here is why.

Let “y” be the number defined by the first sentence, and let “x” be the second number. By this rationale, we can say:

x + y = 34

It’s hard to solve for two different variables, but we do know some things about “y.”

“Four more than five times another,” if defined in terms of x, translates to this

y = 5x + 4

Now that we know what “y” equals in terms of “x,” we can plug it back into our first equation and solve for x.

x + (5x +4) = 34
6x = 30
x=5

So x=5, and y = 5x +4 = 29.