Questions: The price of a gift plus a 19% delivery charge comes to a total cost of 20.23. What was the price of the gift?

The price of a gift plus a 19% delivery charge comes to a total cost of 20.23. What was the price of the gift?
Transcript text: The price of a gift plus a $19 \%$ delivery charge comes to a total cost of $\$ 20.23$. What was the price of the gift? Step 1 of 2: Describe the above situation as a linear equation using " $x$ " or " $y^{\prime \prime}$ as variable names to describe the unknowns.
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Solution

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Solution Steps

To find the price of the gift before the delivery charge, we can set up a linear equation. Let \( x \) be the price of the gift. The total cost is the price of the gift plus 19% of the gift price as the delivery charge. This can be expressed as \( x + 0.19x = 20.23 \). Simplifying, we get \( 1.19x = 20.23 \). We can solve this equation for \( x \) to find the price of the gift.

Step 1: Set Up the Equation

Let \( x \) be the price of the gift. The total cost, including a 19% delivery charge, can be expressed as: \[ x + 0.19x = 20.23 \] This simplifies to: \[ 1.19x = 20.23 \]

Step 2: Solve for \( x \)

To find the price of the gift, we divide both sides of the equation by \( 1.19 \): \[ x = \frac{20.23}{1.19} \] Calculating this gives: \[ x = 17.0 \]

Final Answer

The price of the gift is \\(\boxed{x = 17.0}\\).

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