direct variation grade9 module 3 by mr. joel garcia | PPT - Free Printable

Let's solve the problem step by step using direct variation, as shown in the image.

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Problem:

Julio's wages vary directly with the number of hours he works. If his wage for 5 hours is $1000, how much will he earn in 30 hours?

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Step One: Find points in table

We are given:

| X (hours) | Y (wages) |
|-----------|-----------|
| 5 | 1000 |
| 30 | ? |

So, we know:
- When $ x = 5 $, $ y = 1000 $
- We need to find $ y $ when $ x = 30 $

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Step Two: Find the constant of variation

In a direct variation, the relationship is:

$$
y = kx
$$

Where:
- $ y $ is the dependent variable (wages)
- $ x $ is the independent variable (hours)
- $ k $ is the constant of variation

To find $ k $, use the known values:

$$
k = \frac{y}{x} = \frac{1000}{5} = 200
$$

✔ So, the constant of variation $ k = 200 $

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Step Three: Use the equation to find the unknown

Now that we know $ k = 200 $, use the formula:

$$
y = kx = 200 \times 30 = 6000
$$

✔ So, Julio will earn $6000 in 30 hours.

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✔ Final Answer:

$6000

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🔍 Explanation:

Since wages vary directly with hours, the ratio of wages to hours is constant. This means:
- For every hour, Julio earns $200.
- So in 30 hours: $ 30 \times 200 = 6000 $

This is a classic example of direct variation: as one quantity increases, the other increases proportionally.

✔️ The solution uses the direct variation model: $ y = kx $, where $ k $ is the constant rate of pay.