 # Directly Proportional – Explanation & Examples

##  What does Directly Proportional Mean?

Direct proportion is the relationship between two variables whose ratio is equal to a constant value. In other words, direct proportion is a situation where an increase in one quantity causes a corresponding increase in the other quantity, or a decrease in one quantity results in a decrease in the other quantity.

Sometimes, the word proportional is used without the word direct, just know that they have a similar meaning.

## Directly Proportional Formula

Direct proportion is denoted by the proportional symbol (∝). For example, if two variables x and y are directly proportional to each other, then this statement can be represented as x ∝ y.

When we replace the proportionality sign (∝) with an equal sign (=), the equation changes to:

x = k * y or x/y = k, where k is called non-zero constant of proportionality.

In our day-to-day life, we often encounter situations where a variation in one quantity results in a variation in another quantity. Let’s take a look at some of the real-life examples of directly proportional concept.

• The cost of the food items is directly proportional to the weight.
• Work done is directly proportional to the number of workers. This means that, more workers, more work and les workers, less work accomplished.
• The fuel consumption of a car is proportional to the distance covered. Example 1

The fuel consumption of a car is 15 liters of diesel per 100 km. What distance can the car cover with 5 liters of diesel?

Solution

• Fuel consumed for every 100 km covered = 15 liters
• Therefore, the car will cover (100/15) km using 1 liter of the fuel

If 1 liter => (100/15) km

• What about 5 liters of diesel

= {(100/15) × 5} km

= 33.3
Therefore, the car can cover 33.3 km using 5 liters of the fuel.

Example 2

The cost of 9 kg of beans is $166.50. How many kgs of beans can be bought for$ 259?

Solution

• $166.50 = > 9 kg of beans • What about$ 1 => 9/166.50 kg
Therefore the amount of beans purchased for $259 = {(9/166.50) × 259} kg • =14 kg Hence, 14 kg of beans can be bought for$259

Example 3

The total wages for 15 men working for 6 days are $9450. What is the total wages for 19 men working for 5 days? Solution Wages of 15 men in 6 days =>$ 9450
The wage in 6 days for 1 worker = >$(9450/15) The wage in 1 day for 1 worker =>$ (9450/15 × 1/6)
Wages of 19 men in a day => $(9450 × 1/6 × 19) The total wages of 19 men in 5 days =$ (9450 × 1/6 × 19 × 5)
= $9975 Therefore, 19 men earn a total of$ 9975 in 5 days.

### Practice Questions

1. If the total daily wages of $7$ women or $5$ men is $\$525$. What will be the total daily wage of$13$women and$7$men? 2. Jackie and her sister are going on a road trip. She noted that her car consumes$6.8$L for every$102$km. How far can Jackie’s car if its tank contains$30$L? 3. In Ryan’s construction company, it costs him$\$7, 200$ to pay for the wages of $12$ workers who are working for $6$ days. How much does it cost Ryan’s company to pay for the wages of $18$ staff working for $5$ days?

4. Alice is known for her handcrafted soaps. It costs her $\$540$to create$12$cured bars of soaps each weighing$2.5$kilograms. How much will it cost her to create$24$bars of soaps but this time, weighing$3$kilograms? 5. Felix is studying a city map that is represented with a scale of$1:30000$(with units of cm : m). He noticed that two blocks are$8$cm apart on the map, what is the actual distance between the two blocks? 6. A$12$-meter flag post casts a shadow of$8$meters. What is the height of a flag post that casts a shadow of$18$m? 7. A train takes$8$hours to cover$600$kilometers. How long will it take to cover$1500$kilometers? 8. In a zero-waste store, it costs$\$120$ to refill $12$ jars of body scrub each weighing $800$ g. How much would it cost to refill $36$ jars of body scrub each weighing one kilogram?