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 full of water. If 35 litres are tapped off, the tank is full. Determine the volume
of water in a full tank.

Ask by John May. in South Africa

Jan 19,2025

Question

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 full of water. If 35 litres are tapped off, the tank is full. Determine the volume
of water in a full tank.

Ask by John May. in South Africa

Jan 19,2025

UpStudy AI · Accepted Answer

Sure, let's solve the problem step by step by setting up and solving the appropriate equations.

### **Problem Statement**

A tank is $$ \frac{2}{3} $$ full of water. If 35 liters are tapped off, the tank is $$ \frac{1}{6} $$ full. Determine the volume of water in a full tank.

### **Step 1: Define the Variable**

Let:
- $$ V $$ = Total volume of the tank when it's completely full (in liters).

### **Step 2: Express the Given Information in Terms of $$ V $$**

1. **Initial Volume of Water:**
   - The tank is $$ \frac{2}{3} $$ full.
   - Volume of water initially = $$ \frac{2}{3}V $$.

2. **Volume After Tapping Off 35 Liters:**
   - After removing 35 liters, the tank becomes $$ \frac{1}{6} $$ full.
   - Volume of water after tapping off = $$ \frac{1}{6}V $$.

### **Step 3: Set Up the Equation**

The difference between the initial volume and the volume after tapping off 35 liters should equal 35 liters:

$$
\frac{2}{3}V - 35 = \frac{1}{6}V
$$

### **Step 4: Solve the Equation for $$ V $$**

1. **Subtract $$ \frac{1}{6}V $$ from both sides to isolate terms with $$ V $$:**

$$
\frac{2}{3}V - \frac{1}{6}V = 35
$$

2. **Find a common denominator to combine the terms:**

$$
\frac{4}{6}V - \frac{1}{6}V = 35
$$

$$
\frac{3}{6}V = 35
$$

$$
\frac{1}{2}V = 35
$$

3. **Multiply both sides by 2 to solve for $$ V $$:**

$$
V = 35 \times 2
$$

$$
V = 70 \, \text{liters}
$$

### **Conclusion**

The volume of water in a full tank is **70 liters**.
The full tank holds 70 liters of water.

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