In a full rotation, 360°, a point on the edge of a gear would travel a distance equal to its circumference. The circumference of a circle is:
C=2πr, and since we are only traveling 150°, we need to set up an appropriate ratio for circumference to the distance the point travels:
d/C=150/360
d=5C/12 and since C=2πr
d=10πr/12
d=5πr/12, and since r=4in
d=5*4π/12 in
d=20π/12 in
d=5π/3 in
d≈5.24 in (to nearest hundredth of an inch)
19.70-13=6.7
6.7/0.05=134
600+134=734
So in April she sent 734 text messages
First, create an equation with the criteria given.
If we let x be your number,

(

is twice the product of 3 and x, and if it exceeds

by 10, then we add 10 to

to make the two sides of the equation equal.)
Now, solve for

.