Question

20 POINTS!!!

If A varies directly as B and inversely as C and when A = 6, B = 10 and C = 15. Calculate C when A = 92 and B= 107

Answer 1

C = 963/92

Explanation:

Given :

• A ∝ B
• A ∝ 1/C

Finding the constant of variation, k

• A = kB/C
• 6 = k(10)/(15) [Given in 1st part of question]
• 6 = 2k/3
• 2k = 18
• k = 9

Finding C

• Using the same equation, and new values of A and B, we can find C
• A = kB/C
• C = kB/A
• C = 9 x 107 / 92
• C = 963/92

Answer 2

C =
`(963)/(92)`

Explanation:

given A varies directly as B and inversely as C then the equation relating them is

A =
`(kB)/(C)` ← k is the constant of variation

to find k use the condition A = 6 , B = 10 , C = 15 , then

6 =
`(x10k)/(15)` ( multiply both sides by 15 )

90 = 10k ( divide both sides by 10 )

9 = k

A =
`(9B)/(C)` ← equation of variation

when A = 92 and B = 107 , then

92 =
`(9(107))/(C)` ( multiply both sides by C )

92C = 963 ( divide both sides by 92 )

C =
`(963)/(92)`