Two equations and a ratio?

Algebra Level 2

If 4 a − 18 b + 13 c = 0 4a-18b+13c=0 and 3 a + 3 b − 4 c = 0 3a+3b-4c=0 find the ratio a : b : c . a:b:c.

Submit your answer as a + b + c . a+b+c.


The answer is 14.

Aaryan Maheshwari by Aaryan Maheshwari , 16, India

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1 solution

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Jul 7, 2018

4 a − 18 b + 13 c = 0 ⋯ ( 1 ) , 3 a + 3 b − 4 c = 0 ⋯ ( 2 ) 4a-18b+13c=0\cdots(1),3a+3b-4c=0\cdots(2)

( 1 ) + 6 ( 2 ) → 22 a = 11 c , a : c = 1 : 2 (1)+6(2)\rightarrow22a=11c,a:c=1:2

4 a − 18 b + 13 c = 2 c − 18 b + 13 c = 0 , b : c = 5 : 6 , a : b : c = 3 : 5 : 6 4a-18b+13c=2c-18b+13c=0,b:c=5:6,a:b:c=3:5:6

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