(8) Assessment Practice - Kate's dad gives each of his 5 children an equal part of \( \$ 340 \) to buy gifts. Kate adds 528 to her portion. She finds classic DVDs for \( \$ 8 \) each. How many DVDs can Kate buy? Explain how you solve, Use one or more equations and bar diagrams in your explanation. Tell what your variables represent. (

To solve the problem, we will follow these steps: 1. **Extract known conditions:** - Total amount of money: \( \$ 340 \) - Number of children: \( 5 \) - Additional amount Kate adds to her portion: \( \$ 528 \) - Cost of each DVD: \( \$ 8 \) 2. **Define variables:** - Let \( x \) be the amount of money each child receives from their dad. - Let \( y \) be the total amount of money Kate has after adding her portion and the additional amount. 3. **Calculate the amount each child receives:** Since the total amount is divided equally among the 5 children, we can express \( x \) as: \[ x = \frac{340}{5} \] 4. **Calculate Kate's total amount:** Kate's total amount \( y \) can be expressed as: \[ y = x + 528 \] 5. **Determine how many DVDs Kate can buy:** The number of DVDs \( n \) that Kate can buy is given by: \[ n = \frac{y}{8} \] Now, let's perform the calculations step by step. ### Step 1: Calculate \( x \) \[ x = \frac{340}{5} \] ### Step 2: Calculate \( y \) \[ y = x + 528 \] ### Step 3: Calculate \( n \) \[ n = \frac{y}{8} \] Now, I will perform these calculations. Calculate the value by following steps: - step0: Calculate: \(\frac{340}{5}\) - step1: Reduce the numbers: \(\frac{68}{1}\) - step2: Calculate: \(68\) Calculate or simplify the expression \( (340/5) + 528 \). Calculate the value by following steps: - step0: Calculate: \(\left(\frac{340}{5}\right)+528\) - step1: Divide the terms: \(68+528\) - step2: Add the numbers: \(596\) Calculate or simplify the expression \( ((340/5) + 528)/8 \). Calculate the value by following steps: - step0: Calculate: \(\frac{\left(\left(\frac{340}{5}\right)+528\right)}{8}\) - step1: Remove the parentheses: \(\frac{\left(\frac{340}{5}\right)+528}{8}\) - step2: Divide the terms: \(\frac{68+528}{8}\) - step3: Add the numbers: \(\frac{596}{8}\) - step4: Reduce the fraction: \(\frac{149}{2}\) Now that we have performed the calculations, let's summarize the results: 1. **Amount each child receives (\( x \)):** \[ x = 68 \] Each child receives \( \$ 68 \). 2. **Total amount Kate has after adding her portion (\( y \)):** \[ y = 68 + 528 = 596 \] Kate has \( \$ 596 \). 3. **Number of DVDs Kate can buy (\( n \)):** \[ n = \frac{596}{8} = 74.5 \] Since Kate cannot buy half a DVD, she can buy \( 74 \) DVDs. ### Conclusion: - **Variables:** - \( x \): Amount each child receives from their dad (\$68). - \( y \): Total amount Kate has after adding her portion (\$596). - \( n \): Number of DVDs Kate can buy (74 DVDs). ### Explanation: - Kate's dad gives each child an equal share of the total amount, which is calculated by dividing \( \$ 340 \) by \( 5 \). - After receiving her share, Kate adds \( \$ 528 \) to it, giving her a total of \( \$ 596 \). - Finally, to find out how many DVDs she can buy, we divide her total amount by the cost of each DVD, which is \( \$ 8 \). Since she can only buy whole DVDs, she can purchase \( 74 \) DVDs.