Scientific Understanding

**What sections should I know before attempting to learn this section?**

—> Introduction to Problem Solving

**How do you solve density word problems?**

To help further your problem solving skills, I will introduce you to the concept of density. Density is the mass per unit volume. Another way to state that is the mass divided by the volume. See equation below:

Density = | mass |

volume | |

1 | |

D = | m |

V |

The letter D represents Density, the letter m represents mass, and the letter V represents volume. The density equation has 3 variables. That means in a problem where you have to use density, you will be given 2 variables and asked to solve for the 3^{rd}. Density can have different units like (g/mL) or (g/L) or (kg/L) or (mg/mL) just to name a few. How do we use it to solve some equations? Look to the demonstrated examples below.

**VIDEO Density Problem Solving Demonstrated Example 1**: What is the density for a mass that is 345g and 789mL?

**Step 1: highlight number and units**

What is the density for a mass that is 345g and 789mL?

**Step ****2****: write numbers and units**

mass = 345g

volume = 789mL

**Step ****3****: restate the question**

density = ?

**Step 4****: **

Now what is a formula or concept that relates together mass, volume, and density?

Answer: the density formula (so write down the density formula below)

D = | m |

V |

**Step ****5****:**

What next?

Answer: fill in the numbers and units from your steps 1 through 3.

D = | 345g |

789mL |

**Step ****6****:**

Solve for density (D)

Answer: 245g / 789mL = 0.437g/mL

**Step ****7****:**

COMPLETE ANSWER: D = 0.437g/mL

**VIDEO Density Problem Solving Demonstrated Example 2**: What is the volume of an object that is 154g and has a density of 67g/L?

**Step 1: highlight numbers and units**

What is the volume of an object that is 154g and has a density of 67g/L?

**Step ****2****: write numbers and units**

mass = 154g

density = 67g/L

**Step ****3****: restate question**

volume = ?

**Step ****4****:**

Now what is a formula or concept that relates together mass, volume, and density?

Answer: the density formula (so write down the density formula below)

D = | m |

V |

**Step ****5****:**

What next?

Answer: fill in the numbers and units from your steps 1 through 3.

67g/L = | 154g |

V |

**Step ****6****:**

How do you solve for volume?

Answer: First multiply both sides by V

V * 67g/L = | 154g * V |

V |

**Step ****7****:**

Cross out V on the right side

V * 67g/L = | 154g * V |

V |

**Step ****8****:**

Simplify

V * 67g/L = | 154g |

1 |

**Step ****9****:**

Now divide both sides by 67g/L (red)

V * 67g/L = | 154g |

67g/L | 67g/L |

**Step ****10****:**

Cross out 67g/L on the left side

V * 67g/L = | 154g |

67g/L | 67g/L |

**Step ****11****:**

Simplify

V = | 154g |

67g/L |

**Step ****12****:**

Solve for V

Answer: 154 / 67 = 2.30 L

**Step ****1****3****:**

COMPLETE ANSWER: V = 2.30 L

**PRACTICE PROBLEMS**: Solve for the missing variable in the word problem.

What is the density of an object with a mass of 25g and a volume of 47mL?

Answer: 0.53g/ml

What is density of something that is 36L and 97g?

Answer: 2.69g/L

What is the mass of a cube that has a density of 42g/mL and a volume of 520mL?

Answer: 21840g

An object is 34L and 369g/L. What is the mass of the object?

Answer: 12546g

What is the volume of an object that has a density of 74g/mL and a mass of 58g?

Answer: 0.78ml

If an object is 23kg and 4kg/L. What is the volume?

Answer: 5.75L