13. Meiling was given \( \$ 4 \) pocket money every day of the week. She spent \( \$ 3 \) per day from Monday to Friday and saved the rest. She saved all her pocket money on Saturday and Sunday. Starting on a Monday, how many days did it take her to save \( \$ 55 \) ?

To determine how many days it took Meiling to save \( \$ 55 \), let's break it down step by step. Meiling receives \( \$ 4 \) daily, and from Monday to Friday, she spends \( \$ 3 \). - Daily savings from Monday to Friday: \[ 4 - 3 = 1 \text{ dollar saved per day} \] - Total savings from Monday to Friday over 5 days: \[ 5 \text{ days} \times 1 \text{ dollar} = 5 \text{ dollars} \] On Saturday and Sunday, she saves all of her pocket money. - Savings for Saturday and Sunday: \[ 4 + 4 = 8 \text{ dollars saved over the weekend} \] Now, let's calculate her total savings week-by-week: - After Week 1 (7 days): \[ 5 \text{ (from Mon-Fri)} + 8 \text{ (from Sat-Sun)} = 13 \text{ dollars} \] To reach \( \$ 55 \), we can calculate how many weeks it would take: - Total savings after \( n \) weeks: \[ 13n \] Set this equal to \( 55 \): \[ 13n \geq 55 \] Calculating \( n \): \[ n \approx \frac{55}{13} \approx 4.23 \] This means she would need at least 5 weeks to exceed \( \$ 55 \). Calculating exact days: - After 4 complete weeks, she would have: \[ 13 \times 4 = 52 \text{ dollars} \] - She needs \( 55 - 52 = 3 \) more dollars. In the 5th week: - On Monday, she saves \( 1 \) dollar. - On Tuesday, \( 1 \) dollar. - On Wednesday, \( 1 \) dollar. By Wednesday, she would have saved an additional \( 3 \) dollars, achieving her goal. Thus, she would take \( 28 \text{ (days of 4 weeks)} + 3 \text{ (additional days)} = 31 \text{ days}\) in total. Therefore, it took her **31 days** to save \( \$ 55 \).