Find total number of integers.
![a_1=10,a_n=60,d=1 \\a_n=a_1+(n-1)d \\60=10+(n-1)1 \\n-1=50 \\n=51](https://tex.z-dn.net/?f=a_1%3D10%2Ca_n%3D60%2Cd%3D1%20%5C%5Ca_n%3Da_1%2B%28n-1%29d%20%5C%5C60%3D10%2B%28n-1%291%20%5C%5Cn-1%3D50%20%5C%5Cn%3D51)
Find how many integers is divisible by 2.
![a_1=10,a_n=60,d=2 \\a_n=a_1+(n-1)d \\60=10+(n-1)2 \\2(n-1)=50 \\n-1=25 \\n=26](https://tex.z-dn.net/?f=a_1%3D10%2Ca_n%3D60%2Cd%3D2%0A%5C%5Ca_n%3Da_1%2B%28n-1%29d%0A%5C%5C60%3D10%2B%28n-1%292%0A%5C%5C2%28n-1%29%3D50%0A%5C%5Cn-1%3D25%0A%5C%5Cn%3D26)
Eliminate even numbers.
11, 13, 15,..., 57, 59
This array contains 51 - 26 = 25 numbers.
Eliminate numbers before the first number divisible by 3 and after the last number divisible by 3.
15, 17, 19,..., 55, 57
This array contains 25 - 3 = 22 numbers.
Now we should eliminate numbers divisible by 3: 15, 21, 27...
![a_1=15,a_n=57,d=6,n=? \\a_n=a_1+(n-1)d \\57=15+(n-1)6 \\6(n-1)=42 \\n-1=7 \\n=8](https://tex.z-dn.net/?f=a_1%3D15%2Ca_n%3D57%2Cd%3D6%2Cn%3D%3F%0A%5C%5Ca_n%3Da_1%2B%28n-1%29d%0A%5C%5C57%3D15%2B%28n-1%296%0A%5C%5C6%28n-1%29%3D42%0A%5C%5Cn-1%3D7%0A%5C%5Cn%3D8)
There are 8 such numbers.
Therefore, there are 25 - 8 = 17 numbers that <span>can be evenly divided by neither 2 nor 3</span>
I’m not completely sure about the answers but i can say this: every month adrienne get 5 new dollars. so if it was at like 2 months and $10 (for example) the next month (month 3) she would have $15
How to simplify : keep on dividing the numbers until you get to the lowest number.
EX: Simplify 36
What number goes into 36..... 9!
so 36/9
=4