The enlargement will be 9 inches in wide.
Explanation:
Given that, Wayne has a recipe on a 3-inch by 5-inch index card that he wants to be large to 15 inches long. And, need to find out the how wide will the enlargement be (L). The width and length of index card vary directly. So, this can express as below,
![L \propto W](https://img.qammunity.org/2020/formulas/mathematics/middle-school/fwr203u7twk6u5zzinct1c19ovq1omc71o.png)
L = k W
Here, given L = 3 and W= 5, so
![3=k(5)](https://img.qammunity.org/2020/formulas/mathematics/middle-school/el9evbsvl2fgxwrc0hujt4socc85gpfhgm.png)
![k=(3)/(5)](https://img.qammunity.org/2020/formulas/mathematics/middle-school/r1vtdj8zxu7qnxqy41hrku60vwfkvw35ar.png)
Now, find L with W = 15 as below,
![L=\left((3)/(5)\right) * 15=3 * 3=9 inches](https://img.qammunity.org/2020/formulas/mathematics/middle-school/ukwznlpqq6d2wjq493xwg4byqu6ptlm8z8.png)