Geela and Funky had a total of 620 candies. Geela gave 38 candies to Funky Funky then gave 50 candies to Geela. In the end. Geela has equal number of candies as Funky. How many candies did Geela have at first? Hint: What remains unchanged?

Let's denote the number of candies Geela had at first as \( G \) and the number of candies Funky had at first as \( F \). From the given information: 1. Geela and Funky had a total of 620 candies: \( G + F = 620 \) 2. Geela gave 38 candies to Funky: \( G - 38 \) 3. Funky gave 50 candies to Geela: \( F + 50 \) 4. In the end, Geela has an equal number of candies as Funky: \( G - 38 = F + 50 \) We can set up a system of equations to solve for the number of candies Geela had at first. Let's solve the system of equations: 1. \( G + F = 620 \) 2. \( G - 38 = F + 50 \) Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}G+F=620\\G-38=F+50\end{array}\right.\) - step1: Solve the equation: \(\left\{ \begin{array}{l}F=620-G\\G-38=F+50\end{array}\right.\) - step2: Substitute the value of \(F:\) \(G-38=620-G+50\) - step3: Simplify: \(G-38=670-G\) - step4: Move the variable to the left side: \(G-38+G=670\) - step5: Add the terms: \(2G-38=670\) - step6: Move the constant to the right side: \(2G=670+38\) - step7: Add the numbers: \(2G=708\) - step8: Divide both sides: \(\frac{2G}{2}=\frac{708}{2}\) - step9: Divide the numbers: \(G=354\) - step10: Substitute the value of \(G:\) \(F=620-354\) - step11: Simplify: \(F=266\) - step12: Calculate: \(\left\{ \begin{array}{l}F=266\\G=354\end{array}\right.\) - step13: Check the solution: \(\left\{ \begin{array}{l}F=266\\G=354\end{array}\right.\) - step14: Rewrite: \(\left(F,G\right) = \left(266,354\right)\) The solution to the system of equations is \( F = 266 \) and \( G = 354 \). Therefore, Geela had 354 candies at first.