Question
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Randall buys 3 tickets for a concert for \( \$ 14.50 \) each. He gives the cashier a \( \$ 5 \) bill. How much change does he get? Write equations to show your work.

Ask by Bob Greene. in the United States
Jan 31,2025

Real Tutor Solution

Tutor-Verified Answer

Answer

Randall spends $43.50 on 3 concert tickets at $14.50 each. He gives the cashier a $5 bill. The change he receives is $-38.50.

Solution

To find the change Randall gets after buying 3 tickets for a concert, we need to calculate the total cost of the tickets and then subtract the cost from the amount he gave the cashier. Let's denote: - \( C \) as the cost of one ticket - \( T \) as the total cost of 3 tickets - \( A \) as the amount Randall gave the cashier - \( C \) as the change Randall gets Given: - \( C = \$14.50 \) - \( T = 3 \times C \) - \( A = \$5 \) We can write the following equations to show the work: 1. Total cost of 3 tickets: \[ T = 3 \times C \] 2. Change Randall gets: \[ C = A - T \] Now, we can substitute the values into the equations and solve for the change Randall gets. Calculate the value by following steps: - step0: Calculate: \(3\times 14.5\) - step1: Multiply the numbers: \(43.5\) Calculate or simplify the expression \( 5-43.5 \). Calculate the value by following steps: - step0: Calculate: \(5-43.5\) - step1: Subtract the numbers: \(-38.5\) After buying 3 tickets for a concert at $14.50 each, Randall gives the cashier a $5 bill. The total cost of the tickets is $43.50. Therefore, the change Randall gets is $-38.50.

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The Deep Dive

First, let's calculate the total cost of the 3 concert tickets. The cost per ticket is \( \$ 14.50 \), so we multiply that by 3: Total Cost = \( 3 \times 14.50 = 43.50 \) Now, Randall gives the cashier a \( \$ 5 \) bill, but obviously, \( \$ 5 \) is not enough to cover the cost. So, Randall would actually need to pay in different bills. To calculate how much more Randall needs: Amount Due = Total Cost - Amount Paid Amount Due = \( 43.50 - 5 = 38.50 \) Since Randall gave only \( \$ 5 \), he would need to get the remaining balance in larger denominations to pay the total. But if we were to switch gears, assuming he had paid with a sufficient total (for example, \( \$ 50 \)), the change would then be calculated as follows: Total Payment = \( 50 \) Change = Total Payment - Total Cost Change = \( 50 - 43.50 = 6.50 \) In conclusion, since Randall cannot just give \$5 for tickets costing \$43.50, the simplest answer would be that he needs more money to pay the total.

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