1. **State the problem:** Julie started with 20 pieces of gum and gave away $x$ pieces. Conrad started with 35 pieces and gave away twice as many as Julie, which is $2x$ pieces. We need to find how many pieces Julie gave away when they had the same number of pieces left. 2. **Set up the expressions for gum left:** - Julie's gum left: $20 - x$ - Conrad's gum left: $35 - 2x$ 3. **Set the gum left equal to each other:** $$20 - x = 35 - 2x$$ 4. **Solve for $x$:** Add $2x$ to both sides: $$20 - x + 2x = 35 - 2x + 2x$$ $$20 + x = 35$$ Subtract 20 from both sides: $$x = 35 - 20$$ $$x = 15$$ 5. **Interpretation:** Julie gave away 15 pieces of gum when they had the same number of pieces left. 6. **Check:** - Julie left: $20 - 15 = 5$ - Conrad left: $35 - 2(15) = 35 - 30 = 5$ They both have 5 pieces left, confirming the solution. **Final answer:** Julie gave away **15** pieces of gum.