6. Applied Verbal Problems

Mathematics is really about solving problems, not just about moving letters and numbers around.

Most real-world problems are stated using words and we need to translate them into mathematical statements.

You need to:


For this section, you will need to know:

We will see how to solve each problem using two methods:

You can decide which method you understand best, but if you can follow the simultaneous equations method, it is probably best for future problems.

Good luck!

Example 1

water tank and pipes
Tank and pipes.
Source: Sustainable sanitation

Water is being drained out of a tank through 2 pipes at the rate of 330L/min. We know that one pipe releases 50L/min more than the other. How much do the 2 pipes drain each?


Solution A: Using one variable:

Solution B: Using 2 variables and simultaneous equations:

Example 2

beam
Builders constructing roof beams.

A beam is being supported by 2 pillars. The downwards force (due to gravity) must equal the sum of the 2 upwards forces due to the 2 pillars. Such a system is said to be in equilibrium. The second of the two forces is 6.4 N more than the first and the third is four times the first.

What are the 3 forces? (We are taking the positive magnitude of the forces only.)

Vocabulary

Sometimes a question will have some words which you may not know. In this question:

Pillar: A support column.

Equilibrium: Forces are in "equilibrium" if they cancel each other out.

Beam: A beam is normally made of timber, steel or concrete and holds up a roof (or similar).

Before answering this question, let's look at a query from a reader.

Reader's Question

Dale wrote:

How can the the third force and first force be three times the first force? I just don't get it. How can the first force be three times it self when it is equal to its self? It just confused me.

Solution A: Using one variable:

Solution B: Using 3 variables and simultaneous equations:

Example 3

vial containing drug
Vial of liquid.
Source: Helena Liu, Flickr

A vial contains 2 g of a drug which is required for two dosages. One of the patients is a small child and the other is a large adult who needs to get 660 mg more of the drug than the child. How much should be administered to each?

(Vocabulary: A vial is a container for storing liquid).


Solution A: Using one variable:

Solution B: Using 2 variables and simultaneous equations:

Example 4

scooter
Scooter
Source: RaeAllen

The manufacturer of a scooter engine recommends a gasoline-oil fuel mixture ratio of 15 to 1. In a particular garage, we can buy pure gasoline and a gasoline-oil mixture, which is 75% gasoline.

How much gasoline and how much of the gasoline-oil mix do we need to make 8.0 L of fuel for the scooter engine?


Solution A: Using one variable:

Solution B: Using 2 variables and simultaneous equations:

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