Answer:
374 marbles
Explanation:
Paul (P) has 1/5 this was given
Shawn (S) has 3/8 this was given
That means Tim (T) must have 17/40 because 1/5 + 3/8 = 23/40 and 1- 23/40 = 17/40
Those are the fractional amounts each boy has. We can set up an equation based on the information in the problem to get the total number of marbles (M). Tim has 84 marbles more than Paul. Thus, Tim has a greater number of marbles. 84 more, to be exact. Our equation would then look like this:
P+84=T
Because we have three unknowns, we need three equations. Thus, we need two more, but we can get them from our fractions at the top.
We need to have a question where we find the total number of marbles.
We know that Paul has 1/5 of the marbles. We can use M to represent the total number of marbles.
P = (1/5)M
T= (17/40)M
We had this from before: P+84=T
If we substitute into the equation:
(1/5)M + 84 = (17/40)M
Now there is only one variable in the equation and we can solve for M.
For M, I got 1120/3 which simplifies to 373 and 1/3, since there cannot be 1/3 of a marble, we can round to 374. There are three hundred, seventy-four marbles in the box.
If you want to check the answer, you can put (1120/3) back in for M in the third equation and you will see that each side is equivalent.