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

Accepted Solution

Answer:15 textbooks are in EnglishStep-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 = 45Now 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 and3/4t are English.We also know that number of books in English is 35.  Therefore,     4/5n + 3/4t = 35Now 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 to16n + 15t = 700Let'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 to15n + 700 - 16n = 675Solve for n:-n = -25 son = 25Now 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 and16(25) + 15t = 700 and400 + 15t = 700 and15t = 300 sot = 20If t = 20, then in the expression3/4t, which is the number of textbooks in English,3/4(20) is 15