The larger of two numbers is one more than twice the smaller. Four times the larger is the same as less than nine times the smaller. What's the larger number

9

Step-by-step explanation:

Let larger number be L

and

smaller number be S

The larger is 1 more than twice smaller, so we can write:

L = 1 + 2S

4 times larger is 9 times smaller, so we can write:

4L = 9S

Let's put 1st equation in 2nd and solve for S first:

4L = 9S

4 (1 + 2S) = 9S

4 + 8S = 9S

S = 4

Now,

L = 1 + 2S

L = 1 + 2 (4)

L = 9

The larger number is, thus, equal to 9