She needs 15 purple rectangles for 3 scarves
From the question, we have that 5/7 of the 7 rectangles will be purple
So, we have it that the number of purple rectangles in each scarve will be;
[tex]\frac{5}{7}\times7\text{ = 5}[/tex]So in each scarve, there are 5 purple rectangles
In 3 scarves, the number of purple rectangles will be;
[tex]5\text{ }\times3\text{ = 15}[/tex]