SOLUTION: If x-3 is directly proportional to the square of y and x =5 when y=2, What is x when y=6

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Question 1209464: If x-3 is directly proportional to the square of y and x =5 when y=2,
What is x when y=6
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
The way the language works, if taking variation constant as k,
x-3=ky%5E2

Using the given data,
5-3=k%2A2%5E2
2=4k
k=1%2F2

So the model becomes x-3=%281%2F2%29y%5E2

x-3=%281%2F2%296%5E2
x-3=18
highlight%28x=21%29

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The response from the other tutor shows a formal solution using the definition of direct variation to find the constant of proportionality and solves the problem from there.

That is a good approach, and it would probably be the best approach if we needed to find the solutions for several different sets of data.

But when the problem only requires us to find the answer for a single new set of data, we can use the definition of direct variation to solve the problem informally and quickly.

In this problem, we are given that (x-3) is directly proportional to the square of y; and we are asked to find the value of x when y is 6, given that x is 5 when y is 2.

So the y value increases by a factor of 3 (from 2 to 6); since (x-3) is directly proportional to the square of y, the value of (x-3) increases by a factor of 3^2 = 9.

Originally, the value of x-3 was 5-3 = 2; 2 increased by a factor of 9 is 2*9 = 18.

So the new value of x-3 is 18, which means the new value of x is 18+3 = 21.

ANSWER: 21