Solving a decimal word problem using a linear equation of the form Ax $+\dots$

Susan got a prepaid debit card with $\mathrm{\$}15$ on it. For her first purchase with the card, she bought some bulk ribbon at a craft store. The price of the ribbon was 12 cents per yard. If after that purchase there was $\mathrm{\$}9.24$ left on the card, how many yards of ribbon did Susan buy?
Wyards
$\times 5$

Step 1 ：Translate the problem into a mathematical equation. The initial amount on the card is $15.Thepriceoftheribbonis$0.12 per yard. After the purchase, there is $9.24 left on the card. We can set up the equation as follows: Initial amount - (price per yard * number of yards) = remaining amount.

Step 2 ：Substitute the given values into the equation: $15-(0.12\ast yards)=$9.24.

Step 3 ：Solve the equation for 'yards'.

Step 4 ：$15-0.12\times \text{yards}=9.24$

Step 5 ：$0.12\times \text{yards}=15-9.24$

Step 6 ：$\text{yards}=\frac{15-9.24}{0.12}$

Step 7 ：Calculate the value of 'yards'.

Step 8 ：$\text{yards}=\frac{5.76}{0.12}$

Step 9 ：$\text{yards}=48$

Step 10 ：Final Answer: Susan bought $\boxed{{\displaystyle 48}}$ yards of ribbon.