Word problem, algebra

Question

Blues vary inversely as purples cubed. When there are 250 blues, there are 2 purples. How many blues are present when there are 5 purples?

Answer 1

Let's assume B= Blue and P= Purple

Blues are inversely related to purples cubed so you cannformula :

B=k/(P)^3

Given B=250 and P=2 we can find constant k through any formula.

250=k/(2)^3

250=k/8

250.8=k

2000=k

In next step P=5 is given and k=2000 so we can find B.

B=k/(P)^3

B=2000/(5)^3

B=2000/125

B=16

Answer : Blue =16

Answer 2

Suppose you denote by B the Blues and by P the Purples. It says that blues are inversely related to purples cubed. This we can denote by,

B * P^3 = constant.

It is said that when B = 250, P = 2. So we have 250 * 2^3 = constant. Lets not simplify it just yet.

Now they are asking the value for B, when P = 5. This is the same as B * 5^3 = constant. So,

B * 5^3 = constant = 250 * 2^3, which means

B * 125 = 250 * 2^3

B = 250 * 8 / 125 = 16.

Note: When two variables are inversely related, the product of the two variables is a constant. When two variables are directly related, one variable divided by the other is a constant. The constant is kind of irrelevant, as seen in this example.