Question

Paul, Shaun, and Tim have a box of marbles. Paul has 1/5 of the marbles, Shaun has 3/8 of the remainder, and Tim has the rest of the marbles. Tim has 84 marbles more than Paul. How many marbles are in the box?

Answer 1

By setting up equations based on the proportions of marbles Paul, Shaun, and Tim have and using the fact that Tim has 84 more marbles than Paul, we can calculate that the total number of marbles in the box is 280.

Step-by-step explanation:

The question asks how many marbles are in a box, given the proportions belonging to Paul, Shaun, and Tim, and the fact that Tim has 84 marbles more than Paul. Let's denote the total number of marbles in the box as 'M'. Paul has 1/5 of M, so we have:

(1/5) * M = marbles Paul has

Now, after removing Paul's share, the remainder is 4/5 of M. Shaun then has 3/8 of this remainder, which can be calculated as:

(3/8) * (4/5) * M = (3/10) * M = marbles Shaun has

Since Tim has all the rest, and he has 84 more than Paul, we can set up the following equation:

M - (1/5) * M - (3/10) * M = (1/5) * M + 84

Solving this equation for M gives us:

(1/2) * M = (1/5) * M + 84

(1/2) * M - (1/5) * M = 84

(5/10 - 2/10) * M = 84

(3/10) * M = 84

M = 84 / (3/10)

M = 84 * (10/3)

M = 28 * 10

M = 280

Therefore, there are 280 marbles in the box.