31.4k views
4 votes
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?

User Mattyb
by
8.5k points

1 Answer

1 vote

Answer:

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

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 =
(\frac{20} {100} * A) + A = 0.2A + A = 1.2A

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) =
A - ((40)/(100) * A) = A - 0.4A = 0.6A

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.

User Petar Ivanov
by
6.6k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.