Question: User: 2. Bowling
Bowling Alley A charges a 25 lane fee plus 4 per game. Bowling Alley B charges a 10 lane fee plus 7 per game.
Write a system of equations to represent this relationship. Graph the equations and use the graph to determine the number of games that would cost the same at each bowling alley.
Be sure to use let statements to define variables!
1. **State the problem:**
We want to find the number of games where the total cost at Bowling Alley A equals the total cost at Bowling Alley B.
2. **Define variables:**
Let $x$ = number of games played.
Let $y$ = total cost.
3. **Write the cost equations for each alley:**
- Bowling Alley A: $y = 25 + 4x$
- Bowling Alley B: $y = 10 + 7x$
4. **Set the equations equal to find when costs are the same:**
$$25 + 4x = 10 + 7x$$
5. **Solve for $x$:**
$$25 + 4x = 10 + 7x$$
$$25 - 10 = 7x - 4x$$
$$15 = 3x$$
$$x = \frac{15}{3}$$
$$x = 5$$
6. **Interpretation:**
At $x = 5$ games, the total cost is the same at both alleys.
7. **Find the total cost at $x=5$:**
Using Alley A's equation:
$$y = 25 + 4(5) = 25 + 20 = 45$$
Using Alley B's equation:
$$y = 10 + 7(5) = 10 + 35 = 45$$
Both costs are $45$.
**Final answer:**
The cost is the same when playing 5 games, and the total cost is 45.