Chapter 12 Sequences and Series - 12.2 Analyze Arithmetic Sequences and Series - 12.2 Exercises - Mixed Review - Page 809: 88

23 hats

Suppose $x$ is the number of hats sold and $y$ is the number of scarves sold. Set up the equations. $x+y= 42$ and $16x+18y =710$ We need to add $-16$ times in the first equation. $-16x-16y= -672$ and $16x+18y =710$ This gives: $2y =38 \implies y=19$ Now, $x+19= 42$ This gives: $x=23$ Hence, $x=23$ hats and $y=19$ scarves.