Question

Determine whether quantities vary directly or inversely and find the constant of variation. How much does 3.25m of silk ribbon cost if 0.8m costs $5.60?

Answer 1

we are given

0.8m of silk ribbon costs $5.60

now, we can find cost of 1m of silk ribbon

so, we can divide both sides by 0.8

1 m of silk ribbon cost =$\frac{5.60}{0.8}$

1 m of silk ribbon cost =$7$

Let's assume amount of silk ribbon as x

Let's assume cost of silk ribbon as y

so, we will also get

$y=7x$

so, we can see that

These quantities vary directly

now, we can compare it with

$y=kx$

where k is constant of variation

so,

The constant of variation:

$k=7$

Cost at 3.25m:

we can plug x=3.25 and find y

$y=7*3.25$

$y=22.75$

So, the cost of 3.25m silk ribbon is $22.75........Answer

Answer 2

$22.75 is the answer..

3.25 / 0.8 = 4.06 * $5.60 = $22.75

I hope this helped :)