Questions: A family paid 33,150 as a down payment for a home. If this represents 17% of the price of the home, find the price of the home.

Solution Steps

To find the price of the home, we can use the relationship between the down payment and the percentage it represents of the total price. Specifically, we can set up the equation where 17% of the total price equals $33,150. Solving for the total price will give us the answer.

We know that the down payment of \$33,150 represents 17% of the total price of the home. We can express this relationship mathematically as: \[ \text{down\_payment} = \frac{17}{100} \times \text{total\_price} \]

To find the total price, we rearrange the equation: \[ \text{total\_price} = \frac{\text{down\_payment}}{\frac{17}{100}} = \text{down\_payment} \times \frac{100}{17} \]

Substituting the known value of the down payment: \[ \text{total\_price} = 33150 \times \frac{100}{17} \]

Calculating the total price gives: \[ \text{total\_price} = 33150 \times 5.882352941176471 \approx 195000 \]

Final Answer