Indirect Variation

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#13916

Indirect/Inverse Variation

 $$y \: \alpha \: \frac{1}{x}$$

$$y =\frac{k}{x}$$

where y varies indirectly/inversely with x and k is the constant of variation

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#13918

The number of tables that can be set in a restaurant is inversely proportional to the distance between the tables. When tables are placed 1.2 metres apart 40 tables can be set.
a. Write an equation relating the number of tables (n) and their distance (d) apart.
b. Calculate how many tables can be set when the distance between tables is reduced to 800mm.

a. n $$\alpha$$ ¹/_d

40 = ^k/_1.2

k = 48

∴ n= ⁴⁸/_d

b.  800mm = 0.8m

n = ⁴⁸/_0.8

n = 60

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#13919

The office internet speed (kbps) varies inversely with the number of people using the internet at the same time. If the speed is 12kbps when 40 people are using their computers (and the net), how many extra people would be using the net if the speed drops to 10kpbs?

$$s\alpha\frac{1}{n}$$
$$12=\frac{k}{40}$$
k = 480

∴ $$s=\frac{480}{n}$$

$$10=\frac{480}{n}$$

10n = 480

n = 48

extra people = 48 – 40

∴ 8 extra people using the internet

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#13920

500 soldiers in an army base had enough food for 30 days. After 6 days, some soldiers were sent to another baset and thus the food lasted for 32 more days. How many soldiers left the base?

before they transferred, there was enough food now for 500 soldiers for (30 – 6) days = 24 days

d α $$\frac{1}{s}$$

$$24=\frac{k}{500}$$

k = 15000

$$d=\frac{12000}{s}$$

$$32=\frac{12000}{s}$$

$$s=\frac{12000}{32}$$

s = 375

so if 375 soldiers remain then 500 – 375  = 125 left

∴ 125

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#13921

A hostel has enough food for 125 students for 16 days. How long will the food last if 75 more students join them?

$$d\alpha\frac{1}{s}$$
$$16=\frac{k}{125}$$
k = 2000

∴ $$d=\frac{2000}{s}$$

there are 125 and 75 more join = 125 + 75
= 200

$$d=\frac{2000}{200}$$

d = 10

∴ 10 days

extra people = 48 – 40

∴ 8 extra people using the internet

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#18817

If 32 men can turf a field in 16 days, in how many days can 20 men turf the same field?

$$d\alpha\frac{1}{m}$$

$$d=\frac{k}{m}$$

$$16=\frac{k}{32}$$

k = 512

$$d=\frac{512}{m}$$

$$d=\frac{512}{20}$$

d = 25.6 days

 

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