Question

If "a" varies directly as "b" in each of the following then complete the table.

иσ sραm♡~

(Question given in the attachment)​

Answer 1

Answer:

a=20,25,30,50,80,100,110

Step-by-step explanation:

A) 20+5=25

25+10=30

30+20=50

50+30=80

80+20=100

100+10=110

i guess

part b

Answer 2

★ Concept :-

Here the concept of Direct Variation of a and b has been used. We see that we are given a table where certain values of a and b are given. We see in column 2 value of both a and b are given. This we can take as standard value. Then since a and b vary directly, we can take the values of table and thus find the answer by equating them witb standard value since ratio of a and b will be equal since a and b vary directly.

Let's do it !!

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★ Formula Used :-

$\;\boxed{\sf{\pink{\dfrac{a_{1}}{b_{1}}\;=\;\bf{\dfrac{a_{2}}{b_{2}}}}}}$

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★ Solution :-

Given,

(here we have named the values of a and b according to their position)

• For the values of a ::

» a₁ = 20

» a₂ = 25

» a₃ = _____

» a₄ = 50

» a₅ = _____

» a₆ = 100

» a₇ = _____

• For the values of b ::

» b₁ = ______

» b₂ = 35

» b₃ = 42

» b₄ = ______

» b₅ = 63

» b₆ = ______

» b₇ = 105

From formula we know that,

$\;\sf{\rightarrow\;\;\dfrac{a_{1}}{b_{1}}\;=\;\bf{\dfrac{a_{2}}{b_{2}}}}$

We can change the value of a and b accordingly to the requirement.

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~ For the value of b₁ ::

By applying the values in the formula, we get

$\;\sf{\Longrightarrow\;\;\dfrac{a_{1}}{b_{1}}\;=\;\bf{\dfrac{a_{2}}{b_{2}}}}$

$\;\sf{\Longrightarrow\;\;\dfrac{20}{b_{1}}\;=\;\bf{\dfrac{25}{35}}}$

$\;\sf{\Longrightarrow\;\;b_{1}\;=\;\bf{\dfrac{20\:\times\:35}{25}}}$

$\;\sf{\Longrightarrow\;\;b_{1}\;=\;\bf{\dfrac{20\:\times\:7}{5}}}$

$\;\sf{\Longrightarrow\;\;b_{1}\;=\;\bf{4\:\times\:7}}$

$\;\underline{\boxed{\bf{\purple{\Longrightarrow\;\;b_{1}\;=\;\bf{28}}}}}$

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~ For the value of a₃ ::

By applying values in the formula, we get

$\;\sf{\Longrightarrow\;\;\dfrac{a_{3}}{b_{3}}\;=\;\bf{\dfrac{a_{2}}{b_{2}}}}$

$\;\sf{\Longrightarrow\;\;\dfrac{a_{3}}{42}\;=\;\bf{\dfrac{25}{35}}}$

$\;\sf{\Longrightarrow\;\;a_{3}\;=\;\bf{\dfrac{25\:\times\:42}{35}}}$

$\;\sf{\Longrightarrow\;\;a_{3}\;=\;\bf{\dfrac{5\:\times\:42}{7}}}$

$\;\sf{\Longrightarrow\;\;a_{3}\;=\;\bf{5\:\times\:6}}$

$\;\underline{\boxed{\bf{\red{\Longrightarrow\;\;a_{3}\;=\;\bf{30}}}}}$

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~ For the value of b₄ ::

$\;\sf{\Longrightarrow\;\;\dfrac{a_{4}}{b_{4}}\;=\;\bf{\dfrac{a_{2}}{b_{2}}}}$

$\;\sf{\Longrightarrow\;\;\dfrac{50}{b_{4}}\;=\;\bf{\dfrac{25}{35}}}$

$\;\sf{\Longrightarrow\;\;b_{4}\;=\;\bf{\dfrac{50\:\times\:35}{25}}}$

$\;\sf{\Longrightarrow\;\;b_{1}\;=\;\bf{2\:\times\:35}}$

$\;\underline{\boxed{\bf{\purple{\Longrightarrow\;\;b_{4}\;=\;\bf{70}}}}}$

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~ For the value of a₅ ::

$\;\sf{\Longrightarrow\;\;\dfrac{a_{5}}{b_{5}}\;=\;\bf{\dfrac{a_{2}}{b_{2}}}}$

$\;\sf{\Longrightarrow\;\;\dfrac{a_{5}}{63}\;=\;\bf{\dfrac{25}{35}}}$

$\;\sf{\Longrightarrow\;\;a_{5}\;=\;\bf{\dfrac{25\:\times\:63}{35}}}$

$\;\sf{\Longrightarrow\;\;a_{5}\;=\;\bf{\dfrac{5\:\times\:63}{7}}}$

$\;\sf{\Longrightarrow\;\;a_{5}\;=\;\bf{5\:\times\:9}}$

$\;\underline{\boxed{\bf{\red{\Longrightarrow\;\;a_{5}\;=\;\bf{45}}}}}$

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~ For the value of b₆ ::

$\;\sf{\Longrightarrow\;\;\dfrac{a_{6}}{b_{6}}\;=\;\bf{\dfrac{a_{2}}{b_{2}}}}$

$\;\sf{\Longrightarrow\;\;\dfrac{100}{b_{6}}\;=\;\bf{\dfrac{25}{35}}}$

$\;\sf{\Longrightarrow\;\;b_{6}\;=\;\bf{\dfrac{100\:\times\:35}{25}}}$

$\;\sf{\Longrightarrow\;\;b_{6}\;=\;\bf{4\:\times\:35}}$

$\;\underline{\boxed{\bf{\purple{\Longrightarrow\;\;b_{6}\;=\;\bf{140}}}}}$

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~ For the value of a₇ ::

$\;\sf{\Longrightarrow\;\;\dfrac{a_{7}}{b_{7}}\;=\;\bf{\dfrac{a_{2}}{b_{2}}}}$

$\;\sf{\Longrightarrow\;\;\dfrac{a_{7}}{105}\;=\;\bf{\dfrac{25}{35}}}$

$\;\sf{\Longrightarrow\;\;a_{7}\;=\;\bf{\dfrac{25\:\times\:105}{35}}}$

$\;\sf{\Longrightarrow\;\;a_{7}\;=\;\bf{25\:\times\:3}}$

$\;\underline{\boxed{\bf{\red{\Longrightarrow\;\;a_{7}\;=\;\bf{75}}}}}$