Solve the following Word Problems. Write equations and then solve the equations. Some of the questions were adapted from (Seeliger \& Mouton, n.d.-a, p. 99) and (Loots et al., 2011, p. 55) and (Seeliger \& Mouton, n.d.-b, p. 34) and (Bothma, 2015, p. 175). a. A tank is \( \frac{2}{3} \) full of water. If 35 litres are tapped off, the tank is \( \frac{1}{6} \) full. Determine the volume of water in a full tank.

Let's break down the problem in a systematic way. Let the total volume of the tank be \( V \) litres. Initially, the tank is \( \frac{2}{3} \) full, meaning it has \( \frac{2}{3} V \) litres of water. After tapping off 35 litres, the water left in the tank is \( \frac{2}{3} V - 35 \). According to the problem, this amount equals \( \frac{1}{6} V \): \[ \frac{2}{3} V - 35 = \frac{1}{6} V \] Now, let's solve for \( V \). First, we'll eliminate the fractions by finding a common denominator, which is 6 in this case. Multiplying each term by 6 gives us: \[ 6 \left( \frac{2}{3} V \right) - 6(35) = 6 \left( \frac{1}{6} V \right) \] This simplifies to: \[ 4V - 210 = V \] Rearranging the equation, we have: \[ 4V - V = 210 \] \[ 3V = 210 \] Now, divide both sides by 3: \[ V = \frac{210}{3} = 70 \] Thus, the volume of water in a full tank is **70 litres**.