Question

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, while Carmen has 40% fewer shells than Alex.

How many shells does each friend have?

Answer 1

Alex has 110 shells

Benji has 132 shells

Carmen has 66 shells

Explanation:

In this question, we are tasked with calculating the number of shells each of the friends have.

We proceed as follows;

Since Alex is the linking point between the other two friends, we say that let the number of shells Alex has be A

Now, Benji has 20% more shells

This mathematically means that the number of shells owned by Benji = (20% × A) + A = 0.2A + A = 1.2A

Carmen has 40% fewer shells than Alex;

Mathematically, this means that the number of shells owned by Carmen is A - (40% × A) = A - 0.4A = 0.6A

To find A, we simply add all together and equate to 308

Mathematically, we have;

A + 1.2A + 0.6A = 308

2.8A = 308

Divide both sides by 2.8

A = 308/2.8

A = 110

This means Alex has 110 shells

Benji has 1.2A = 1.2 × 110 = 132 shells

Carmen has 0.6A = 0.6 × 110 = 66 shells