Arslan and Bilal each have some marbles. Arslan says to Bilal, "If you give me 'x' marbles, we will both have the same number of marbles." Bilal replies, "If you give me twice that amount, I will have 30 marbles more than you." What is the value of 'x'?

Explanation

Let Arslan have A marbles and Bilal have B marbles. When Bilal gives 'x' marbles to Arslan, their amounts become B - x and A + x respectively. Since they become equal, B - x = A + x (Equation 1). When Arslan gives Bilal twice that amount (2x), their amounts become A - 2x and B + 2x. Bilal then has 30 more marbles than Arslan, so B + 2x - (A - 2x) = 30 (Equation 2). Simplifying Equation 2 gives B - A + 4x = 30. From Equation 1, B - A = 2x. Substituting into Equation 2 yields 2x + 4x = 30, so 6x = 30 and x = 5.