Question

Rebecca has a collection of 45 books. The collections consists of novels and textbooks written in either chinese or english. 4/5 of the novels are english. 3/4 of the textbooks are english. The total number of books in english is 35. How many books are textbooks written in english

Answer 1

15

Explanation:

Answer 2

15 textbooks are in English

Explanation:

Begin with the simple algebraic statement:

Rebecca has some novels and some textbooks written in Chinese or English, and the total number of books is 45.

The equation for that, letting n = novels and t = textbooks, is:

n + t = 45

Now go to the next part that says that 4/5 of the novels are in English and 3/4 of the textbooks are in English.

The word "of" means to multiply, and the word "is" means equals, so

4/5n are English and

3/4t are English.

We also know that number of books in English is 35. Therefore,

4/5n + 3/4t = 35

Now we have a system of equations with 2 unknowns. First is to simplify that second one down and get rid of the fractions. Do this by multiplying the whole thing through by 20:

`(20)(4)/(5)n+(20)(3)/(4)t=(20)35` which simplifies to

16n + 15t = 700

Let's solve this for t, then sub that t value back into n + t = 45. Solving for t:

`t=(140)/(3)-(16)/(15)n`

Subbing in for t:

`n+(140)/(3)-(16)/(15)n=45`

Simplify this by multiplying everything through by 15:

`(15)n+(15)(140)/(3)-(15)(16)/(15)n=(15)45`

which simplifies to

15n + 700 - 16n = 675

Solve for n:

-n = -25 so

n = 25

Now we can put that back into the expression that relates the number of novels and texts in English to solve for t:

16n + 15t = 700 and

16(25) + 15t = 700 and

400 + 15t = 700 and

15t = 300 so

t = 20

If t = 20, then in the expression

3/4t, which is the number of textbooks in English,

3/4(20) is 15