Alex, benji, and carmen collect shells they have found on the beach. When combined, they have a total of 308 shells. They also noticed that Benji has 20% more shells than Alex, and Carmen has 40% fewer shells than Alex. How many shells does each friend have?

Alex has 110 shells, Benji has 132 shells and Carmen has 66 shells.

Step-by-step explanation:

The total number of shells gotten by Alex, Benji and Carmen is 308.

Let the number of shells Alex has be A, let the number of shells Benji has be B and let the number of shells Carmen has be C.

=> A + B + C = 308

Benji has 20% more shells than Alex, this means that we add 20% of Alex's shells to the number of shells Alex already has to get the number of shells that Benji has:

B = (20% of A) + A =

Carmen has 40% fewer shells than Alex, that means that we subtract 40% of Alex's shells from the number of shells Alex already has to get the number of shells that Carmen has::

C = A - (40% of A) =

Replacing B and C in the initial equation, we have that:

A + 1.2A + 0.6A = 308

=> 2.8A = 308

A = 308 / 2.8 = 110

∴ B = 1.2 * 110 = 132

and C = 0.6 * 110 = 66

Therefore, Alex has 110 shells, Benji has 132 shells and Carmen has 66 shells.