Stephanie M. answered • 07/14/15
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"x varies directly with y" means that x gets larger as y gets larger.
"x varies indirectly with y" means that x gets smaller as y gets larger.
"x varies jointly with y and z" means that x gets larger as yz gets larger.
So, let's look at each answer choice. Before we do any calculation, we may be able to eliminate some choices.
A) A varies jointly with B and C
At first, B and C are small and A is moderately large. When both B and C get larger, A gets smaller. So, A can't vary jointly with B and C, since otherwise, A should have gotten larger. (A) is likely not the answer.
B) B varies jointly with A and C
At first, A is moderately large and C is small, while B is small. Then, A gets small and C gets much larger, while B gets slightly larger. Finally, C gets much smaller and A gets much larger, while B gets slightly larger. This is plausible. (B) could be the answer.
C) C varies jointly with A and B
At first, A is moderately large and B is small, while C is small. Then, A gets smaller and B gets slightly larger, while C gets much larger. Finally, A and B get larger, while C gets much smaller. That means C doesn't vary jointly with A and B, since otherwise, C should have gotten larger when both A and B did. (C) is likely not the answer.
D) C varies directly with A and inversely with B
At first, C is small and A is moderately large. When A gets smaller, C gets much larger. That means C doesn't vary directly with A, since otherwise, C should have gotten smaller when A did. (D) is likely not the answer.
So, the answer is almost certainly (B). Let's test it:
5 = k(10)(3)
5 = 30k
1/6 = k
8 = k(3)(16)
8 = 48k
1/6 = k
10 = k(15)(4)
10 = 60k
1/6 = k
The constant of variation is the same for all the data we're given. Thus, (B) is the answer.
