Let a, b, and c be integers that satisfy 2a+3b=52, 3b+c=41, and bc=60. Find a+b+ c.
+60 Let's start by finding 3b+c=41
From the problem "bc=60", we know that b and c are both divisors of 60. We can use this to help us solve this.
These are the divisors of 60 if you need them:
1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.
Before looking at what B and C are I want you to try to figure it out...
Ok, "b" is 12, and "c" is 5! 
Now we just have to figure out "a"
"2a+3b=52"
We already know b is 12 so we can rewrite the problem like this
2a + 36 (because 12 times 3 is 36) = 52
Now we just subtract 36 from both sides and we get
2a = 16
Now we just have to divide each side by 2 and...
"a" is 8!
"Find a+b+ c."
Finally, we add up all our numbers
8 + 12 + 5 = 25! 
Hope this helped!
