Question

Determine whether quantities vary directly or inversely and find the constant of variation. If 5 bushels of wheat weigh 136 kg, how much do 3.5 bushels of wheat weigh?

Answer 1

Well if 5 bushels = 136kg then 1 = 27.2 then 3.5 = 95.2 so it is directly and th vriation is 27.2

Answer 2

Let the bushels of wheat is b and weight of the wheat is w.

We can say that more the bushels of wheat more will be the weight of the wheat.

Hence, the quantities  vary directly.

Therefore, we have

$b=kw$,  where k is the constant of variation.

Now, we have been given that 5 bushels of wheat weigh 136 kg. Thus, we have

$5=136k\\ \\ k=\frac{5}{136}$

Thus, the constant of variation is  $\frac{5}{136}$

Now, we have been given 3.5 bushels of wheat. Hence, we have

$3.5=\frac{5}{136} w\\ \\ w=\frac{136\times 3.5}{5} \\ \\ w=95.2$

Therefore, 3.5 bushels of wheat weigh 95.2 kg