Cheapest ball

Let $x$ be the original price of the two balls. Then the new price of the first ball is $x-0.05x=0.95x$ and the new price of the second ball is $x+0.15x=1.15x$ . Given in the problem that, $1.15x-0.95x=6$ , simplifying we get

$0.2x=6$

$x=30$

Therefore, the cheapest ball is $0.95x=0.95(30)=$ $\large \color{#D61F06}\boxed{\$28.5}$

Relevant wiki: Percentages - Problem Solving

Suppose, the original price of each ball is $\$x$

The price of the first ball was reduced by $5\%$ , so it is now $\$(0.95x)$

And the price of the other one was increased by $15\%$ , so it is now $\$(1.15x)$

So the price difference is $\Rightarrow 1.15x - 0.95x = 0.2x$

And we know that it is $\$6.00$

So $0.2x = \$6$

$⇒ x = \$30$

The original price was $\$30$

And the cheapest ball now costs $\$(0.95x) = \$28.50$ or $28.5$