Questions: A car dealership decreased the price of a certain car by 5%. The original price was 49,800. (a) Fill in the blank to write the new price in terms of the original price. Write your answer as a decimal. New price = (blank) × Original price (b) Use your answer in part (a) to determine the new price. New price: (blank) (blank)

A car dealership decreased the price of a certain car by 5%. The original price was 49,800. (a) Fill in the blank to write the new price in terms of the original price. Write your answer as a decimal. New price = (blank) × Original price (b) Use your answer in part (a) to determine the new price. New price: (blank) (blank)
Transcript text: A car dealership decreased the price of a certain car by $5 \%$. The original price was $\$ 49,800$. (a) Fill in the blank to write the new price in terms of the original price. Write your answer as a decimal. New price $=$ $\square$ $\times$ Original price (b) Use your answer in part (a) to determine the new price. New price: $\$ \square$ $\square$
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Solution

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Solution Steps

Step 1: Convert the Percentage Change to Decimal

To convert the percentage change -5% to a decimal, we divide it by 100. Thus, $$d = \frac{-5}{100} = -0.05$$

Step 2: Calculate the New Price

The new price can be calculated using the formula: $$\text{{New price}} = P \times (1 + d)$$ Substituting the given values, we get: $$\text{New price} = 49800 \times (1 - 0.05) = 47310$$

Final Answer:

The new price of the car after the -5% change is $47310.

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