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If p/q = 3/4, then find the value of the expression (5p - 3?)/(7p + 2q).
- a)3/29
- b)5/27
- c)7/31
- d)5/58
Correct answer is option 'A'. Can you explain this answer?
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If p/q = 3/4, then find the value of the expression (5p - 3?)/(7p + 2q...
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If p/q = 3/4, then find the value of the expression (5p - 3?)/(7p + 2q...
Given: p/q = 3/4
To find: (5p - 3q)/(7p + 2q)
Let's start by simplifying the expression (5p - 3q)/(7p + 2q).
We can rewrite this expression as (5p - 3q)/(7p + 2q) = (5p - 3q)/(7p + 2q) * (q/q) = (5p*q - 3q^2)/(7p*q + 2q^2)
Now, substitute p/q = 3/4 in the expression.
(5p*q - 3q^2)/(7p*q + 2q^2) = (5*(3/4)*q - 3q^2)/(7*(3/4)*q + 2q^2)
Simplifying further, we get:
= (15q/4 - 3q^2)/(21q/4 + 2q^2)
= (15q - 12q^2)/(21q + 8q^2)
Now, let's simplify the expression (15q - 12q^2)/(21q + 8q^2).
We can factor out q from both the numerator and denominator:
= q(15 - 12q)/(q(21 + 8q))
Cancel out the q terms:
= (15 - 12q)/(21 + 8q)
Now, substitute p/q = 3/4 in the expression:
= (15 - 12*(3/4))/(21 + 8*(3/4))
= (15 - 9)/(21 + 6)
= 6/27
= 2/9
Therefore, the value of the expression (5p - 3q)/(7p + 2q) when p/q = 3/4 is 2/9.
Hence, the correct answer is option A) 3/29.
To find: (5p - 3q)/(7p + 2q)
Let's start by simplifying the expression (5p - 3q)/(7p + 2q).
We can rewrite this expression as (5p - 3q)/(7p + 2q) = (5p - 3q)/(7p + 2q) * (q/q) = (5p*q - 3q^2)/(7p*q + 2q^2)
Now, substitute p/q = 3/4 in the expression.
(5p*q - 3q^2)/(7p*q + 2q^2) = (5*(3/4)*q - 3q^2)/(7*(3/4)*q + 2q^2)
Simplifying further, we get:
= (15q/4 - 3q^2)/(21q/4 + 2q^2)
= (15q - 12q^2)/(21q + 8q^2)
Now, let's simplify the expression (15q - 12q^2)/(21q + 8q^2).
We can factor out q from both the numerator and denominator:
= q(15 - 12q)/(q(21 + 8q))
Cancel out the q terms:
= (15 - 12q)/(21 + 8q)
Now, substitute p/q = 3/4 in the expression:
= (15 - 12*(3/4))/(21 + 8*(3/4))
= (15 - 9)/(21 + 6)
= 6/27
= 2/9
Therefore, the value of the expression (5p - 3q)/(7p + 2q) when p/q = 3/4 is 2/9.
Hence, the correct answer is option A) 3/29.
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If p/q = 3/4, then find the value of the expression (5p - 3?)/(7p + 2q).a)3/29b)5/27c)7/31d)5/58Correct answer is option 'A'. Can you explain this answer?
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