What does Tom's solution of x = 32.5 mean in the context of the situation?
Understand the Problem
The question is asking about the implications of the value found for x in the equation used to calculate the original cost of a bicycle. Specifically, it seeks to interpret what Tom's conclusion of x = 32.5 means in relation to the financial details of George's bicycle purchase and sale.
Answer
George paid $32.50 for the broken bicycle.
Answer for screen readers
George paid $32.50 for the broken bicycle.
Steps to Solve
- Interpreting the equation
The equation given is $2x + 20 = 85$, where $x$ represents the original cost of the bicycle. The term $2x$ indicates that George's selling price ($85) is $20 more than twice what he paid for the bicycle.
- Solving for $x$
We already know from the problem that Tom solved the equation and found $x = 32.5$. This means the original cost of the bicycle needs to be interpreted in the context of the situation.
- Finding the original cost
To find the original cost, we substitute $x$ back into the context. The equation $2x + 20 = 85$ can also be interpreted as:
- $2(32.5) + 20 = 85$.
Calculating gives:
$$ 65 + 20 = 85 $$
This confirms that George paid $32.50 for the bicycle.
George paid $32.50 for the broken bicycle.
More Information
The value $32.5$ represents the original cost that George incurred when purchasing the bicycle. Since he sold it for $85, we can also see that George made a good profit after the repairs and resale.
Tips
- A common mistake could be misinterpreting the meaning of $x$. It's easy to confuse the value of $x$ with profit or selling price rather than identifying it as the original purchase price.
- Another mistake could involve incorrectly adding or miscalculating the components of the equation.
