The desired number is the difference between the number of messages sent by the 16th day and the number sent by the 9th day:
... n = t(16) - t(9)
... n = (40×√16) - (40×√9)
... n = 40×(4 - 3) = 40
40 text messages were sent between the ninth and sixteenth day of the month.
The key: make the base of two side the same,,,
then: for the same base, the exponents are equal.
36
Add all the sides up
15+15=30
3+3=6
30+6=36
We have to set up 2 different equations if we are to solve for 2 unknowns. The first equation is x = y + 4. One number (x) is (=) 4 more than another (y + 4). Since we have determined that x is larger (cuz it's 4 more than y), when we set up their difference, we are going to subtract y from x cuz x is bigger. The second equation then is

. In our first equation we said that x = y + 4, so let's sub that value in for x in the second equation:

. Expand that binomial to get

. Of course the y squared terms cancel each other out leaving us with 8y + 16 = 64. Solving for y we get that y = 6. Subbing 6 in for y in our first equation, x = 6 + 4 tells us that x = 10. Yay!