A baseball problem

$Let\quad the\quad bat\quad cost\quad x\$\quad and\quad the\quad ball\quad y\$\quad$

$so,\quad x+y=1.10$

$and\quad x=1+y$

$putting\quad x=1+y\quad in\quad first\quad equation,\quad we\quad get$

$1+1+y=1.10$

$\Rightarrow 1+2y=1.10$

$\Rightarrow 2y=0.1$

$\Rightarrow y=\boxed{ 0.05 }$

If the bat costs $ $1.00$ more than the ball and the total price is $ $1.10$ , then:

$x + x + 1.00 = 1.10$

$2x + 1.00 = 1.10$

$2x = 1.10 - 1.00$

$2x = 0.10$

$x = \boxed {0.05}$