2/5 of Ian's marbles is equal to 3/7 of Roy's marbles. If Roy has 55 more marbles than Ian, how many marbles do Ian and Roy have in all?

Answer 1

I believe there is a typo in the question as solving the problem as is would have Ian having 55 more marbles than Roy. We can still solve this as a logic problem to arrive at the same intended answer.

Let I stand for # of Ian's marbles and R stand for # of Roy's marbles.

Equation #1: We know that 2/5 I = 3/7 R

Equation #2: We also know that I = R + 55 because Roy has 55 more marbles than Ian

Equation #3: We want to know how many marbles Ian and Roy have together I + R = ?

In equation #1 let's solve for one of the variables, say R.

2/5 I = 3/7 R Now multiply both sides by 5 to get rid of denominator

2 I = 15/7 R Now multiply both sides by 7 to get rid of the other denominator

14 I = 15 R Solve for R

14/15 I = R (Re: TYPO, you can see this says that Roy, not Ian, would have the lesser marbles. But continuing on...)

Let's plug in this value of R into equation #2

I = R + 55 where R = 14/15 I

I = (14/15 I) + 55 Now multiply both sides by 15 to get rid of the denominator

15 I = 14 I + 825 Isolate the I-variable

15 I - 14 I = 825

I = 825

Ian has 825 marbles

Go back to equation #2

I = R + 55 where I = 825

825 = R + 55

825 - 55 = R

770 = R

Equation #3: I + R = ?

770 + 825 = 1,595 marbles total