Question

HELP PLEASE, ASAP!

Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.


Kayla and Dayton, both teachers, are adding books to their class libraries. Kayla's classroom started out with a collection of only 18 books, but she plans to purchase an additional 2 books per week. Dayton's library started out with 9 books, and he has enough money in his budget to purchase another 3 books per week. At some point, the two teachers' libraries will contain the same number of books. How many books will each class have? How many weeks will that take?

Answer 1

Let x represents the number of week and y represents the total number of book.

As per the given statement:

Kayla's classroom started out with a collection of only 18 books, but she plans to purchase an additional 2 books per week.

"2 books per week" means 2x

⇒
`y = 18 + 2x` .....[1]

It is also given that Dayton's library started out with 9 books, and he has enough money in his budget to purchase another 3 books per week.

"3 books per week" means 3x

⇒
`y = 9+ 3x` .....[2]

at some points, the two teachers' libraries will contain the same number of books.

⇒
`18+2x = 9 + 3x`

Subtract 9 from both sides we get;

`9+2x =3x`

Subtract 2x from both sides we have;

`9 =x`

y = 18 + 2x = 18 + 2(9) = 18 + 18 = 36

Therefore,

• 36 books will each class have.

• 9 weeks will that take.