Good News Café is selling two new drinks, Refreshing and Cheerful. The cost of preparing each of these drinks is \(70\text{ cents}\) and \(\$1.05\) respectively.
On Monday, the café sold \(x\) cups of Refreshing and \(y\) cups of Cheerful with a total production cost of \(\$62.30\) for these two drinks. Form an equation in \(x\) and \(y\) and show that it reduces to \(2x + 3y = 178\).[1]
A total of \(73\) cups of Refreshing and Cheerful was sold on that Monday. Form another equation in \(x\) and \(y\) and hence, find the number of cups of each drink sold.[4]