Let a, b, and c be integers that satisfy 2a+3b=52, 3b+c=41, and bc=60. Find a+b+ c.

Guest Apr 14, 2021

#2**+1 **

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!

SirAkko Apr 15, 2021