During the holiday season, Brianna sold scarves at a kiosk in a shopping mall. Embroidered floral scarves cost \( \$ 27 \) each, and sheer chevron scarves cost \( \$ 13 \). One day she sold 42 scarves. Total recelpts for the day were \( \$ 770 \). How many of each kind of scarf did she sell? Brianna sold \( \square \) embroidered floral scarves and \( \square \) sheer chevron scarves.

Let \( x \) be the number of embroidered floral scarves sold, and \( y \) be the number of sheer chevron scarves sold. We can set up the following system of equations based on the information given: 1. The total number of scarves sold: \[ x + y = 42 \] 2. The total revenue from the scarves: \[ 27x + 13y = 770 \] Now, we can solve this system of equations. First, we can solve the first equation for \( y \): \[ y = 42 - x \] Next, we substitute \( y \) in the second equation: \[ 27x + 13(42 - x) = 770 \] Expanding this gives: \[ 27x + 546 - 13x = 770 \] Combining like terms: \[ 14x + 546 = 770 \] Now, subtract 546 from both sides: \[ 14x = 770 - 546 \] \[ 14x = 224 \] Now, divide by 14: \[ x = \frac{224}{14} = 16 \] Now that we have \( x \), we can find \( y \): \[ y = 42 - x = 42 - 16 = 26 \] Thus, Brianna sold \( 16 \) embroidered floral scarves and \( 26 \) sheer chevron scarves. In conclusion: Brianna sold \( 16 \) embroidered floral scarves and \( 26 \) sheer chevron scarves.