23 rd January 2025 Week: 3 Homewerk. 1 1.) Mr. Mensah redrew an amounc of money from the bank. He gave \( 1 / 3 \) of it to the son and gave 15 to the daughter. If he sill had GH \( \$ 200 \) left, how much did he redreio from the bank? And how much did the daughter recenve? Solution

Let's solve the problem step by step. ### **Problem Statement:** Mr. Mensah withdrew an amount of money from the bank. He gave **\( \frac{1}{3} \)** of it to his son and **GHS 15** to his daughter. After these transactions, he still had **GHS 200** left. **Questions:** 1. How much did Mr. Mensah withdraw from the bank? 2. How much did the daughter receive? ### **Solution:** Let's denote the total amount of money Mr. Mensah withdrew from the bank as **\( x \)**. 1. **Amount given to the son:** \[ \frac{1}{3} \times x = \frac{x}{3} \] 2. **Amount given to the daughter:** \[ \text{GHS }15 \] 3. **Amount left after the transactions:** \[ \text{GHS }200 \] Now, according to the problem statement, the sum of the amounts given to the son, the daughter, and the amount left should equal the total amount withdrawn: \[ \frac{x}{3} + 15 + 200 = x \] Let's solve for **\( x \)**: 1. Combine like terms: \[ \frac{x}{3} + 215 = x \] 2. Subtract **\( \frac{x}{3} \)** from both sides to isolate the variable: \[ 215 = x - \frac{x}{3} \] 3. Simplify the right side: \[ 215 = \frac{3x}{3} - \frac{x}{3} = \frac{2x}{3} \] 4. Multiply both sides by **\( \frac{3}{2} \)** to solve for **\( x \)**: \[ x = 215 \times \frac{3}{2} = 322.5 \] So, **Mr. Mensah withdrew GHS 322.50** from the bank. ### **Answers to the Questions:** 1. **Total Amount Withdrawn:** \[ \text{GHS }322.50 \] 2. **Amount Given to the Daughter:** \[ \text{GHS }15 \] ### **Summary:** - **Total Withdrawn:** GHS 322.50 - **Daughter Received:** GHS 15