When solving an equation, why must we complete the same computation to BOTH sides of the equation?

Which shows the pre image of triangle xyz

43lbs of tomatos cost $387. how much would 41lbs cost

3women sell hats at a craft fair weekly. the money they make at the fair is split into categories. 9% goes to pay taxes. $55 goes to pay rent for the space they sell in. the rest is split between the women. if the group make $706 at the fair, how much does each women get paid once the money is divided