PDF) Direct Variation Worksheets | natzky pagsidan - Academia.edu - Free Printable

It looks like you've uploaded an image containing a math problem, but the text is not clearly visible or readable in your message. However, based on your description and the partial content I can infer from the text snippet, it seems to be a set of problems involving direct variation (proportional relationships).

Let me interpret and solve the problems assuming they are standard direct variation questions.

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General Concept: Direct Variation

If $ y $ varies directly as $ x $, then:

$$
y = kx
$$

where $ k $ is the constant of proportionality.

We can find $ k $ using known values of $ x $ and $ y $, then use it to find unknowns.

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Let’s go through each part one by one.

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Problem 1:

> Suppose $ y $ varies directly as $ x $, and $ y = 40 $ when $ x = 16 $. Find $ y $ when $ x = 48 $.

Step 1: Use the direct variation formula:
$$
y = kx
$$

Plug in $ y = 40 $, $ x = 16 $:
$$
40 = k \cdot 16 \Rightarrow k = \frac{40}{16} = 2.5
$$

Now use $ k = 2.5 $ to find $ y $ when $ x = 48 $:
$$
y = 2.5 \cdot 48 = 120
$$

✔ Answer: $ y = 120 $

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Problem 2:

> Suppose $ y $ varies directly as $ x $, and $ y = 18 $ when $ x = 3 $. Find $ x $ when $ y = 42 $.

First, find $ k $:
$$
18 = k \cdot 3 \Rightarrow k = \frac{18}{3} = 6
$$

Now use $ y = 42 $:
$$
42 = 6x \Rightarrow x = \frac{42}{6} = 7
$$

✔ Answer: $ x = 7 $

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Problem 3:

> Suppose $ y $ varies directly as $ x $, and $ y = 100 $ when $ x = 4 $. Find $ y $ when $ x = 16 $.

Find $ k $:
$$
100 = k \cdot 4 \Rightarrow k = \frac{100}{4} = 25
$$

Now $ y = 25 \cdot 16 = 400 $

✔ Answer: $ y = 400 $

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Problem 4:

> Suppose $ x $ varies directly as $ z $, and $ x = 7 $ when $ z = 14 $. Find $ x $ when $ z = 18 $.

Note: This is $ x $ varying directly with $ z $, so:
$$
x = kz
$$

Use $ x = 7 $, $ z = 14 $:
$$
7 = k \cdot 14 \Rightarrow k = \frac{7}{14} = 0.5
$$

Now $ x = 0.5 \cdot 18 = 9 $

✔ Answer: $ x = 9 $

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Problem 5:

> Suppose $ y $ varies directly as $ x $, and $ y = 8 $ when $ x = 2000 $. Find $ y $ when $ x = 4 $.

Find $ k $:
$$
8 = k \cdot 2000 \Rightarrow k = \frac{8}{2000} = 0.004
$$

Now $ y = 0.004 \cdot 4 = 0.016 $

✔ Answer: $ y = 0.016 $

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Final Answers Summary:

1. $ y = 120 $
2. $ x = 7 $
3. $ y = 400 $
4. $ x = 9 $
5. $ y = 0.016 $

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