Mis Tham bought z botlles of oil at \( \$ 7 \) each. She gave the cashier \( \$ 50 \) (a) Find the change Mrs Tham recelved in terms of \( z \). (b) \( 11 z=3 \), how much change did Mrs Tham receive?

Given: - Mis Tham bought \( z \) bottles of oil at $7 each. - She gave the cashier $50. (a) To find the change Mrs. Tham received in terms of \( z \), we need to calculate the total cost of the oil bottles and then subtract that from the amount she gave to the cashier. The total cost of the oil bottles is \( 7z \) dollars. The change Mrs. Tham received is the amount she gave to the cashier minus the total cost of the oil bottles: \[ \text{Change} = 50 - 7z \] (b) Given that \( 11z = 3 \), we can solve for \( z \) and then substitute it into the expression for the change to find out how much change Mrs. Tham received. Solving for \( z \): \[ 11z = 3 \] \[ z = \frac{3}{11} \] Substitute \( z = \frac{3}{11} \) into the expression for the change: \[ \text{Change} = 50 - 7 \times \frac{3}{11} \] Now, we can calculate the change Mrs. Tham received. Calculate the value by following steps: - step0: Calculate: \(50-\frac{7\times 3}{11}\) - step1: Multiply the numbers: \(50-\frac{21}{11}\) - step2: Reduce fractions to a common denominator: \(\frac{50\times 11}{11}-\frac{21}{11}\) - step3: Calculate: \(\frac{550}{11}-\frac{21}{11}\) - step4: Transform the expression: \(\frac{550-21}{11}\) - step5: Subtract the numbers: \(\frac{529}{11}\) Mrs. Tham received a change of $48.09 when she bought \( z \) bottles of oil at $7 each and gave the cashier $50.