Question

Omar, amare, and jack paid a total of $68.25 for dinner and tickets to a concert. The concert tickets cost $9.75 each. If the 3 friends split the dinner bill equally, how much did each spend on dinner
To determine the solution arithmetically in 2 steps, first (divide 68.25 by 3 or subtract 9.75 from 68.25 or add 9.75 to 68.25) and then (add 9.75 from the result, or subtract 9.75 to the result, or divide the result by 3). To determine the solution algebraically, set up and solve the equation ( 3x +9.75=68.25, or 3x-9.75=68.25, or 3(x-9.75)=68.25,or3(x+9.75)=68.25

Answer 1

To solve the problem both arithmetically and algebraically, let's first go through the arithmetic solution step by step:

### Arithmetic Solution

1. **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:
\[
3 \text{ tickets} \times 9.75 \text{ dollars/ticket} = 29.25 \text{ dollars}
\]

2. **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.

3. **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 \( x \):

1. **Subtract 29.25 from both sides:**
\[
3x = 68.25 - 29.25
\]
\[
3x = 39.00
\]

2. **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.