Acorns varied directly as walnuts and inversely as squirrels squared.

Question

When there were 28 acorns, there were there were 7 walnuts and 3 squirrels. How many acorns were there when there were 4 walnuts but only 2 squirrels?

Answer 1

When something has a direct relationship, one variable increase and the other also increases.

When something has an inverse relationship, one variable increases and the other decreases.

 

Let number acorns = A

Let number of walnuts = W

Let number squirrels = S

 

Knowing this, we can write a formula.

 

A = KW / S²

 

W = 4

S = 2

K = constant

 

 

We need to solve for K by plugging the initial values.

 

S²A = KW

 

S²A / W = K

 

(3² * 28) / 7 = K

 

(9 * 28) / 7 = K

 

9 * 4 = K

 

36 = K

 

 

Plug in these values into the formula to find A, using K=36 and the other given variables.

 

W = 4

S = 2

 

A = KW / S²

 

A = (36 * 4) / 2²

 

A = (36 * 4) / 4

 

A = 36

 

 

There are 36 squirrels.