Question

If p:q=5:7, p-q=4 , then 3p+4q=?

Answer 1

p:q=5:7
let p=5x
q=7x
then
p-q=-4
5x-7x=-4
x=2
now
p=5×(2)=10
q=7×(2)=14
so 3p+4q=3×(10)+4×(14)=30+56=86

Answer 2

Solution: (After editing the mistake in Q, )

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Given :

p : q = 5 : 7,.

p - q = -4,

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To find :

3p + 4q = ?

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As, we can write the ratio in the form of fraction,.

⇒ $p : q = 5 : 7$

⇒ $\frac{p}{q} = \frac{5}{7}$

⇒ $5q = 7p$

⇒ 7p - 5q = 0   ....(i)                 (As they both are equal)

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We know that,

⇒ p - q = -4  ....(ii)

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If we eliminate one of the variable from the equations,.

We will get the value of the other,

And then, if we substitute the value of the variable,

We will get the value of the variable,

Then if we substitute in the given equation,

We will get the value,.

So,

 7 x (ii) - (i)

⇒ 7 x (p - q) - (7p - 5q) = 7 (-4) - (0)

⇒ 7p - 7q - 7p + 5q = -28

⇒ 7p - 7p - 7q + 5q = -28

⇒ -2q = -28

⇒ q = $\frac{-28}{-2}$

⇒ q = 14
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If we substitute the value in equation (i),.

We get,.

⇒ 7p - 5q = 0

⇒ 7p - 5(14) = 0

⇒ 7p - 70 = 0

⇒ 7p = 70

⇒ p = 10,..

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If we substitute the value in the given equation,

We get,

⇒ 3p + 4q

⇒ 3(10) + 4(14)

⇒ 30 + 56

⇒ 86,..

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∴ The value of the given equation is (3p + 4q) is 86

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