The issue is with "the bat is $1.00 more than the ball." We assume that means price-of-bat is $1.00. It really means price-of-bat = price-of-ball + $1.00. Our brains want to simplify total-cost to price-of-ball + $1.00, but the true cost is price-of-ball + (price-of-ball + $1.00).

If ball is $0.05, then bat is $1.05 (that is, $0.05 + $1.00), bringing the total to $1.10.

Took me a while, too.

The issue is with "the bat is $1.00 more than the ball." We assume that means price-of-bat is $1.00. It really means price-of-bat = price-of-ball + $1.00. Our brains want to simplify total-cost to price-of-ball + $1.00, but the true cost is price-of-ball + (price-of-ball + $1.00).

If ball is $0.05, then bat is $1.05 (that is, $0.05 + $1.00), bringing the total to $1.10.