Elliot has a total of 2626 books. He has 1212 more fiction books than nonfiction books. Let x𝑥 represent the number of fiction books and y𝑦 represent the number of nonfiction books.This system of equations models the number of books.x+y=26x−y=12𝑥+𝑦=26𝑥−𝑦=12Elliot added the two equations and the result was 2x=38.Solve the equation. How many fiction books does Elliot have? fiction booksHow many nonfiction books does Elliot have? nonfiction books
Question
Elliot has a total of 2626 books. He has 1212 more fiction books than nonfiction books. Let x𝑥 represent the number of fiction books and y𝑦 represent the number of nonfiction books.This system of equations models the number of books.x+y=26x−y=12𝑥+𝑦=26𝑥−𝑦=12Elliot added the two equations and the result was 2x=38.Solve the equation. How many fiction books does Elliot have? fiction booksHow many nonfiction books does Elliot have? nonfiction books
Solution
To solve for the number of fiction and nonfiction books Elliot has, we first solve the equation 2x = 38.
Step 1: Divide both sides of the equation by 2 to solve for x.
2x/2 = 38/2
This simplifies to x = 19.
So, Elliot has 19 fiction books.
Next, we substitute x = 19 into the first equation of the system to solve for y.
Step 2: Substitute x = 19 into the equation x + y = 26.
19 + y = 26
Step 3: Subtract 19 from both sides of the equation to solve for y.
y = 26 - 19
This simplifies to y = 7.
So, Elliot has 7 nonfiction books.
Similar Questions
Elliot has a total of 26 books. He has 12 more fiction books than nonfiction books. Let x represent the number of fiction books.Which equation represents the situation? How many fiction books does Elliot have? How many nonfiction books does Elliot have?
Elliot has a total of 26 books. He has 12 more fiction books than nonfiction books. Let x represent the number of fiction books and y represent the number of nonfiction books. Which system of linear equations represents the situation?Responsesx+y=26 and x+y=12x plus y is equal to 26 and x plus y is equal to 12x+y=26 and x−y=12x plus y is equal to 26 and x minus y is equal to 12x−y=26 and x+y=12x minus y is equal to 26 and x plus y is equal to 12x+y=26 and −x+y=12
Two months ago, Bernard had a total of 1,389 books in his bookshop. He sold 644 books last month and 579 books the month before.How many books does he have now?
Ms. Kitts works at a music store. Last week she sold 6 more than 3 times the number of CDs that she sold this week. Ms. Kitts sold a total of 110 CDs over the 2 weeks. Which system of equations can be used to find /, the number of CDs she sold last week, and t, the number of CDs she sold this week?
David bought three DVDs and four books for $40. Anna spent $18 and bought one DVD and six books. Solve the system of equations to determine the cost of each DVD and book.
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.