How to solve it---**Question Stem:** 4. Mrs Tan went to a shop where she spent half of her money and another $10. She then went to a second shop and spent half of her remaining money and another $10. She later went to the third shop and spent half of her remaining money and another $10. She then had $15 left. How much money did Mrs Tan have before she entered the first shop? **Calculations and Notes (Handwritten):** 15 + 10 + 10 = 45 45 * 2 * 2 * 2 (Implied multiplication result not fully shown, but suggests 45 * 8) **Diagram Description:** The diagram consists of handwritten box/bar models and calculations, likely representing a backward working method to solve the problem. - **Upper Section:** Depicts the state related to the third shop and the money left. It shows a box representing $15 (the amount left). Adjacent is another box split into two parts, labeled '10' and '1/2'. Below these boxes, the total length is indicated by a bracket labeled '1/2 units'. Arrows show calculations: one from '15' and '10' pointing to '25' (suggesting 15 + 10 = 25), and another from '25' and a '1/2' section pointing to '45'. There is also a label '35' with an arrow pointing from the '15' and '10' combined section. - **Middle Section:** Shows a single box labeled '45', divided into two equal parts labeled '1/2' and '1/2'. This section seems to represent the amount before the third shop or related calculations. - **Lower Section:** Shows a larger area potentially representing earlier stages. Part of it is a grid-like drawing. To the right, a long box is shown divided into two equal parts, labeled '1/2' and '1/2'. Note: The handwritten calculations and some labels in the diagram (like '45' in the middle section and the final calculation 45 * 2 * 2 * 2) do not directly align with the correct backward calculation steps derived from the problem description (which would involve adding 10 and then doubling at each stage). However, they are part of the extracted image content.

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Let's understand this step-by-step problem. Mrs Tan visits three shops in sequence. At each shop, she spends exactly half of her current money plus an additional ten dollars. After visiting all three shops, she has fifteen dollars remaining. We need to find how much money she had initially before entering the first shop. Let's work backwards from the final amount. Mrs Tan had fifteen dollars left after the third shop. Before entering the third shop, she spent half of her money plus ten dollars, leaving her with fifteen dollars. If we call her money before the third shop 'x', then x minus ten dollars, divided by two, equals fifteen dollars. Solving this equation: x equals fifty dollars before the third shop. Now let's continue working backwards to find the amount before the second shop. We know she had fifty dollars after the second shop. Before entering the second shop, she spent half of her money plus ten dollars, leaving her with fifty dollars. Using the same logic: if x is her money before the second shop, then x minus ten, divided by two, equals fifty. Solving: x equals one hundred twenty dollars. Notice the pattern: add ten, then multiply by two. Finally, let's find Mrs Tan's initial amount. We know she had one hundred twenty dollars after the first shop. Before entering the first shop, she spent half of her money plus ten dollars, leaving her with one hundred twenty dollars. Using our pattern: x minus ten, divided by two, equals one hundred twenty. Solving: x equals two hundred sixty dollars. Therefore, Mrs Tan initially had two hundred sixty dollars before entering the first shop. Let's verify our answer by working forward. Starting with two hundred sixty dollars: At shop one, she spends half which is one hundred thirty dollars, plus ten dollars, leaving one hundred twenty dollars. At shop two, she spends sixty dollars plus ten dollars, leaving fifty dollars. At shop three, she spends twenty-five dollars plus ten dollars, leaving fifteen dollars. Perfect! This confirms our answer is correct. Mrs Tan initially had two hundred sixty dollars.