###### Example 5.2.10 Two Different Interest Rates

Notah made some large purchases with his two credit cards one month and took on a total of \(\$8{,}400\) in debt from the two cards. He didn't make any payments the first month, so the two credit card debts each started to accrue interest. That month, his Visa card charged \(2\%\) interest and his Mastercard charged \(2.5\%\) interest. Because of this, Notah's total debt grew by \(\$178\text{.}\) How much money did Notah charge to each card?