An algebra problem by safa m

Algebra Level 2

If a c − b d a c + b d = 3 11 \dfrac{ ac-bd} { ac+bd} = \dfrac{3}{11} and c d = 2 5 \dfrac{c}{d} = \dfrac{2}{5} , what is the value of a b \dfrac{a}{b} ?

35 8 \frac{35}{8} 6 55 \frac{ 6}{55} 5 17 \frac{5} { 17} 23 13 \frac{ 23}{ 13}

Safa M by safa m , 21, Iran

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2 solutions

Michael Mendrin
Jul 9, 2014

This solution isn't unique. We could have a = 70, b = 16, c = 2, d = 5, and meet the same equations, and yet a + b = 86.

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Kushagra Ramnani
Jul 9, 2014

by cross multiplication, we get- => 11ac-11bd = 3ac+3bd => 14bd = 8ac => 14b/8a = c/d => 7b/4a = 2/5 => 8a = 35b therefore, a=35 and b=8 => a+b = 35+8 = 43

1 Helpful 0 Interesting 0 Brilliant 0 Confused

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