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Mathematics

If (7p + 3q) : (3p - 2q) = 43 : 2, find p : q.

Ratio Proportion

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Answer

Given, (7p + 3q) : (3p - 2q) = 43 : 2.

7p+3q3p2q=4322(7p+3q)=43(3p2q)14p+6q=129p86q92q=115ppq=92115=45.\Rightarrow \dfrac{7p + 3q}{3p - 2q} = \dfrac{43}{2} \\[1em] \Rightarrow 2(7p + 3q) = 43(3p - 2q) \\[1em] \Rightarrow 14p + 6q = 129p - 86q \\[1em] \Rightarrow 92q = 115p \\[1em] \Rightarrow \dfrac{p}{q} = \dfrac{92}{115} = \dfrac{4}{5}. \\[1em]

Hence, the value of ratio p : q is 4 : 5.

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