Question

Alice has 8 stars and earns a new one each week. Mack has 2 stars and get 2 each week. How many weeks before they have the same number of stars?

Answer 1

After $x$ weeks Alice and Mack will have $8+x$ stars and $2+2x$ stars respectively. We need such $x$ that $8+x=2+2x$ .

Solve the equation $8+x=2+2x$; $8+x-2-x=2+2x-2-x$ , that is, $x=6$ (weeks).

Answer: 6 weeks.