The sum of three numbers is 48

Question

The sum of three numbers is 48. The sum of the two larger numbers is three times the smallest. The sum of the two smaller numbers is 6 more than the largest. Find the numbers

Answer 1

Here's what we know:

a + b + c = 48 (three numbers total 48)

b + c = 3a (the two larger numbers total 3 times the smallest)

a + b = c + 6 (the two smaller numbers total the 6 more than the largest)

 

we have a value for b + c, so plug that into the original equation:

a + 3a = 48

4a = 48

a = 12

 

Now we can do the same thing with a + b:

c + 6 + c = 48

2c + 6 = 48

2c = 42

c = 21

 

so that gives us:

12 + b + 21 = 48

You should be able to find b from here.