4 Andreas, Isla and Paulo share some money in the ratios \( 3: 2: 5 \) The total amount of money that Isla and Paulo receive is \( £ 76 \) more than the amount of money that Andreas receives. Andreas buys a video game for \( £ 48.50 \) with some of his share of the money. Work out how much money Andreas has left from his share of the money when he has bought the video game.

To determine how much money Andreas has left after purchasing the video game, let's break down the problem step by step. ### 1. **Understand the Ratios** - **Andreas**, **Isla**, and **Paulo** share money in the ratio **3:2:5**. - Let the common multiplier be **\( x \)**. - **Andreas** receives: \( 3x \) - **Isla** receives: \( 2x \) - **Paulo** receives: \( 5x \) ### 2. **Establish the Relationship** - The total amount that **Isla** and **Paulo** receive together is \( 76 \) pounds more than what **Andreas** receives. - This can be written as: \[ 2x + 5x = 3x + 76 \] \[ 7x = 3x + 76 \] \[ 4x = 76 \quad \Rightarrow \quad x = 19 \] ### 3. **Determine Each Person's Share** - **Andreas**: \( 3x = 3 \times 19 = 57 \) pounds - **Isla**: \( 2x = 2 \times 19 = 38 \) pounds - **Paulo**: \( 5x = 5 \times 19 = 95 \) pounds *Verification*: - **Isla + Paulo**: \( 38 + 95 = 133 \) pounds - **Andreas**: \( 57 \) pounds - Difference: \( 133 - 57 = 76 \) pounds (which matches the given condition) ### 4. **After Purchasing the Video Game** - **Andreas** spends \( 48.50 \) pounds on a video game. - Money left: \( 57 - 48.50 = 8.50 \) pounds **Answer:** £8.50