5. Alissa Duerfeldt purchased a total of 376 shares stock this week. \( \frac{1}{8} \) of the shares purchased was stock i medical supplies, \( \frac{1}{2} \) of the shares purchased was stock a utility company, and \( \frac{3}{8} \) of the shares purchased w. stock in a pet food factory. What were the individu number of shares purchased in each of the thr stocks?

To find the individual number of shares purchased in each of the three stocks, we can set up an equation based on the total number of shares purchased and the fractions of shares purchased in each stock. Let's denote the number of shares purchased in medical supplies as \( M \), the number of shares purchased in the utility company as \( U \), and the number of shares purchased in the pet food factory as \( P \). Given that Alissa purchased a total of 376 shares, we can set up the following equation: \[ M + U + P = 376 \] We also know that: - \( \frac{1}{8} \) of the shares purchased was in medical supplies, so \( M = \frac{1}{8} \times 376 \) - \( \frac{1}{2} \) of the shares purchased was in the utility company, so \( U = \frac{1}{2} \times 376 \) - \( \frac{3}{8} \) of the shares purchased was in the pet food factory, so \( P = \frac{3}{8} \times 376 \) Now, we can substitute these values into the equation to find the individual number of shares purchased in each stock. Calculate the value by following steps: - step0: Calculate: \(376\times \frac{1}{8}+376\times \frac{1}{2}+376\times \frac{3}{8}\) - step1: Multiply the numbers: \(47+376\times \frac{1}{2}+376\times \frac{3}{8}\) - step2: Multiply the numbers: \(47+188+376\times \frac{3}{8}\) - step3: Multiply the numbers: \(47+188+141\) - step4: Add the numbers: \(376\) The individual number of shares purchased in each of the three stocks is: - Medical supplies: \( \frac{1}{8} \times 376 = 47 \) shares - Utility company: \( \frac{1}{2} \times 376 = 188 \) shares - Pet food factory: \( \frac{3}{8} \times 376 = 141 \) shares Therefore, Alissa purchased 47 shares in medical supplies, 188 shares in the utility company, and 141 shares in the pet food factory.