let x = number of books at $0.25
let y = number of books at $0.50
then x + y = 17 books
and $0.25x + $0.50y = $5.75
we solve the first equation for x, which is x= 17 - y
we substitute that value into the second equation, which becomes
$0.25 (17 - y) + $0.50y = $5.75
expanding, we get $4.25 - $0.25y + $0.50y = $5.75
combining, we get $0.25y = $1.50
solving, y = 6
subtracting, we get 17 - 6 = 11
Proof: 6 x $0.50 + 11 x $0.25 = $5.75; $3.00 + $2.75 = $5.75
