Answer:
15 textbooks are in English
Step-by-step 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:
[tex](20)\frac{4}{5}n+(20)\frac{3}{4}t=(20)35[/tex] 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:
[tex]t=\frac{140}{3}-\frac{16}{15}n[/tex]
Subbing in for t:
[tex]n+\frac{140}{3}-\frac{16}{15}n=45[/tex]
Simplify this by multiplying everything through by 15:
[tex](15)n+(15)\frac{140}{3}-(15)\frac{16}{15}n=(15)45[/tex]
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
