C Clever I Connect every student to a world of learning Solving a decimal word problem using a linear equation of the form \( A x+\ldots \) Lucy got a prepaid debit card with \( \$ 30 \) on it. For her first purchase with the card, she bought some bulk ribbon at a craft store. The price of the ribbon was 24 cents per yard. If after that purchase there was \( \$ 23.04 \) left on the card, how many yards of ribbon did Lucy buy? \( \square \) yards

To solve this problem, we can set up a linear equation based on the information given. Let \( x \) represent the number of yards of ribbon Lucy bought. The cost of the ribbon can be calculated as \( 0.24x \) dollars because it costs 24 cents per yard. Since Lucy started with $30 and has $23.04 left after her purchase, we can write the equation: \[ 30 - 0.24x = 23.04. \] Now, let's solve for \( x \). First, subtract 23.04 from both sides: \[ 30 - 23.04 = 0.24x \implies 6.96 = 0.24x. \] Next, divide both sides by 0.24 to isolate \( x \): \[ x = \frac{6.96}{0.24} = 29. \] So, Lucy bought \( 29 \) yards of ribbon. When solving similar problems, it's easy to get the operations mixed up. One common mistake is confusing addition and subtraction on the left side of the equation. Always double-check that you're correctly translating the word problem into a mathematical equation, and pay attention to the details like units (in this case, dollars and yards) to avoid errors.