Ann and betty together have $60. ann has $9 more than twice betty's amount. how much money does each have? ( show work, ! )

To find this out we need to set up a system of equations. I will rewrite the question. While doing this I will put in parenthesis what it means, then we will rewrite what's only in parenthesis.
Ann & Betty together (A + B) have (=) $60 (60). Ann has (A=) 9 more (9+) than twice Betty's amount (2B).
Rewrite what's in parenthesis.
A + B = 60
A = 2B + 9
This is our system of equations.
Since A + B = 60, and 2B + 9 = A, we can safely assume A is significantly larger than B, so A can make up the higher number from 60. A is twice B plus an extra 9, so A can make a little more than half of 60.
A is in the range of 30-40.
We can assume A is an odd number, since it needs 9 taken away, and A - 9 needs to make a difference of a number divisible by 2.
Let's try 37 for A.
Since A is 9 more than twice B, we need to subtract 9 from 37.
37 - 9 = 26.
Now A = 26, so all we have left is to divide by 2 to get B.
26/2 = 13.
Now B = 13. Add the original number of A to B.
37 + 13 = 50.
Close, but we're just short.
Let's try 45 for A.
45 - 9 = 36.
36/2 = 18.
45 + 18 = 63.
Close, but we're just a little too much.
Let's try 39 for A.
39 - 9 = 30.
30/2 = 15.
39 + 15 = 54.
We're just a little short again.
Let's try 41 for A.
41 - 9 = 32.
32/2 = 16.
41 + 16 = 57.
We're still a little short.
Let's try 43 for A.
43 - 9 = 34.
34/2 = 17.
43 + 17 = 60.
We have solved your system of equations.
A = 43.
B = 17.
I hope this helps!