Let's denote the total sales she needs as "X".
The total gross pay consists of two components:
Base pay: $1950
Commission: 6.75% of total sales
So, the equation representing the total gross pay would be:
Base Pay + Commission = Total Gross Pay
$1950 + 0.0675 * X = $4190
Now, let's solve for X:
0.0675 * X = $4190 - $1950
0.0675 * X = $2240
Divide both sides by 0.0675:
X = $2240 / 0.0675
X = $33259.26
Therefore, she would need to have a total sales amount of approximately $33,259.26 in order to achieve a gross pay of $4,190, considering the base pay and the commission percentage.