Question

Sarah lost her science book. Her school charges a lost book fee equal to 75% of the cost of the book. Sarah received a notice stating that she owed the school $60 for he lost book. What is the constant of proportionality? What does it mean in the context of this situation

Answer 1

This constant of proportionality represents the lost fee, which is the relation between both variables.

Explanation:

Givens

• The lost fee is 75% of the cost of the book.
• Sarah owes $60 to the school for the lost book.

Let's call
`c` the cost of the book and
`f` the lost feet. All this can be expressed as

`f=0.75c`

This expression indicates that the lost fee is 75% of the cost of the book.

Notice that this is a linear equation, where
`f` and
`c` are directly proportional and the constant of proportionality is 0.75, which is 75%.

This constant of proportionality represents the lost fee, which is the relation between both variables.

Now, replacing values we can find the cost of the book

`60=0.75c\\c=(60)/(0.75)\\ c=80`

The book costs $80.

Answer 2

Answer: 0.75,

The constant of proportionality is the ratio between two directly proportional quantities.

The cost of book changes but the lost book fee charge remains constantper book i.e.0.75

Explanation:

Given: Let x be the cost of her book (in dollars).

Since, her school charges a lost book fee equal to 75% of the cost of the book.

Then, the the lost book fee=75% of x

Since 75% =0.75

Thus, the the lost book fee=$0.75x

The cost of book changes but the lost book fee charge remains constant per book i.e.0.75

Sarah received a notice stating that she owed the school $60 for he lost book.

The the lost book fee=
`0.75(60)=$45`