If a varies jointly as b and c, and a = -10, when b = 12 and c = 2, how do you find a when b = 8 and c = ½?

1 Answer
Apr 27, 2017

Answer:

#a = -5/3 = -1 2/3#

Explanation:

There are two ways to find the answer, finding the constant of proportionality or just setting up a proportion.

Finding the constant of proportionality :

#a = kbc#

Plug in the first set of numbers to find #k#:

#-10 = k * 12 * 2#

#-10 = 24k#

#k = -10/24 = -5/12#

Now use #k# to find #a#:

#a = -5/12 *8/1 *1/2 = -40/24 = -5/3 = -1 2/3#

Using proportions:

#(a_1)/(a_2) = (b_1 c_1)/(b_2 c_2)#

#(-10)/(a_2) = (12*2)/(8/1*1/2)#

#(-10)/(a_2) = 24/4#

Use the cross product #a/b = c/d#: #" "a*d = b*c#

#-10 * 4 = 24*a_2#

#-40 = 24 * a_2#

#a_2 = -40/24 = -5/3 = -1 2/3#