Find the ratio a:b, if it is given that . . .
a) 6a-3b=5b
b) a+b=3b
c) 2a-3b/5=a+b/3
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SOLUTION:
a: b = 2: 3, b: c = 6: 5
a/b = ⅔ , b/c = 6/5
In the ratio a: b , b = 3 and in the ratio b:c , b=6. We have to make b equal in the two ratios. LCM of 3 and 6 = 3×6. So we multiply the antecedent and consequent of the first ratio by 6 and antecedent and consequent of 2nd ratio by 3
a: b = 2:3 = (2×6) : (3×6) = 12:18
b:c = 6:5 =(6×3) : (5×3)= 18 : 15
Then, a: b: c = 12: 18: 15
a: b: c = 4: 6: 5
Let a, b and c be 4 x, 6 x & 5 x
a + b + c = 30 (Given)
Then, 4 x + 6 x+ 5 x = 30
15 x= 30
x = 30/15
x = 2
The value of a = 4x=4 x 2 = 8, b = 6x=6 x 2= 12 & c =5x = 5 x 2 = 10.
So, the value of 2a + 3b + 4c
= 8 x 2 + 12 x 3 + 4 x 10
= 16 + 36 + 40
= 92.
Hence, the value of 2a+ 3b +4c =92.
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