To solve the problem both arithmetically and algebraically, let's first go through the arithmetic solution step by step:
Arithmetic Solution
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Calculate the total cost of the concert tickets: Since each concert ticket costs $9.75 and there are 3 friends, the total cost for concert tickets is: \[ 3 \text{ tickets} \times 9.75 \text{ dollars/ticket} = 29.25 \text{ dollars} \]
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Subtract the cost of the concert tickets from the total amount: Now, subtract the total cost of the tickets from the total amount spent: \[ 68.25 \text{ dollars} - 29.25 \text{ dollars} = 39.00 \text{ dollars} \] This amount, $39.00, is the total amount spent on dinner.
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Calculate the dinner cost per person: Since the dinner bill is split equally among the 3 friends: \[ \frac{39.00 \text{ dollars}}{3} = 13.00 \text{ dollars} \] Thus, each friend spent $13.00 on dinner.
Algebraic Solution
Let \( x \) represent the amount each friend spent on dinner. We know the following:
- The total amount spent is $68.25.
- The cost for the concert tickets for 3 friends is \( 3 \times 9.75 = 29.25 \).
The total amount spent can be represented as: \[ 3x + 29.25 = 68.25 \]
To solve for \( x \):
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Subtract 29.25 from both sides: \[ 3x = 68.25 - 29.25 \] \[ 3x = 39.00 \]
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Divide by 3: \[ x = \frac{39.00}{3} = 13.00 \]
Thus, each friend spent $13.00 on dinner.
Conclusion
In both the arithmetic and algebraic approaches, we find that each friend spent $13.00 on dinner.
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