SOLUTION: If a varies jointly as b and the square root of c,and a=21 when b=5 and c=3,find a when b=9 and c=225

Question 1149781: If a varies jointly as b and the square root of c,and a=21 when b=5 and c=3,find a when b=9 and c=225
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the general formula for joint variation is a = k * b * c * d * .....
k is the constant of variation.
you are told that a varies jointly as b and tghe square root of c.
the formula for your problem is therefore a = k * b * sqrt(c)
when a = 21 and b = 5 and c = 3, the formula becomes:
21 = k * 5 * sqrt(3)
solve for k to get:
k = 21 / (5 * sqrt(3))
k is the constant of variation.
once solved for, it remains the same in all uses of the formula.
you want to find a when b = 9 and c = 225.
formula of a = k * b * sqrt(c) becomes:
a = 21 / (5 * sqrt(3)) * 9 * sqrt(225)
simplify to get:
a = 21 / (5 * sqrt(3) * 9 * 15
simplify further to get:
a = 21 / (sqrt(3) * 9 * 3
simplify further to get:
a = 21 * 27 / sqrt(3)
simplify further to get:
a = 567 / sqrt(3)
simplify further to get:
a = 567 * sqrt(3) / 3
finally simplify to get:
a = 189 * sqrt(3)

your solution is:
k = 21 / (5 * sqrt(3)) when a = 21 and b = 5 and c = sqrt(3).
a = 189 * sqrt(3) when k = 21 / (5 * sqrt(3)) and b = 9 and c = 225.

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