Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.\newlineA librarian is expanding some sections of the city library. He buys books at a special price from a dealer who charges one price for any hardback book and another price for any paperback book. For the children's section, Mr. Hatfield purchased 2424 new hardcover books and 3737 new paperback books, which cost a total of $303\$303. He also purchased 2424 new hardcover books and 9696 new paperback books for the adult fiction section, spending a total of $480\$480. What is the special price for each type of book?\newlineThe special price is $_\$\_ for hardcover books and $_\$\_ for paperback books.

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 2right chevron icon
Solve a system of equations using elimination: word problemsright chevron icon

Full solution

Q. Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.\newlineA librarian is expanding some sections of the city library. He buys books at a special price from a dealer who charges one price for any hardback book and another price for any paperback book. For the children's section, Mr. Hatfield purchased 2424 new hardcover books and 3737 new paperback books, which cost a total of $303\$303. He also purchased 2424 new hardcover books and 9696 new paperback books for the adult fiction section, spending a total of $480\$480. What is the special price for each type of book?\newlineThe special price is $_\$\_ for hardcover books and $_\$\_ for paperback books.
  1. Define Prices: Let's denote the price of each hardcover book as hh and the price of each paperback book as pp. Mr. Hatfield purchased 2424 hardcover books and 3737 paperback books for the children's section, which cost a total of $303\$303. This gives us the equation 24h+37p=30324h + 37p = 303.
  2. Children's Section Purchase: For the adult fiction section, he purchased 2424 hardcover books and 9696 paperback books, spending a total of $480\$480. This gives us the equation 24h+96p=48024h + 96p = 480.
  3. Eliminate Variable: We now have a system of two equations. We need to eliminate one of the variables, hh or pp. We choose to eliminate hh because it has the same coefficient in both equations.
  4. Solve for Paperback Price: To eliminate hh, we subtract the first equation from the second equation. This gives us 59p=17759p = 177.
  5. Substitute and Solve: We now divide both sides of the equation by 5959 to solve for pp. This gives us p=17759p = \frac{177}{59}, which simplifies to p=3p = 3.
  6. Final Hardcover Price: We substitute p=3p = 3 into the first equation and solve for hh. This gives us 24h+37(3)=30324h + 37(3) = 303. Simplifying the equation, we get 24h+111=30324h + 111 = 303.
  7. Final Hardcover Price: We substitute p=3p = 3 into the first equation and solve for hh. This gives us 24h+37(3)=30324h + 37(3) = 303. Simplifying the equation, we get 24h+111=30324h + 111 = 303. Subtracting 111111 from both sides of the equation, we get 24h=303−11124h = 303 - 111, which simplifies to 24h=19224h = 192.
  8. Final Hardcover Price: We substitute p=3p = 3 into the first equation and solve for hh. This gives us 24h+37(3)=30324h + 37(3) = 303. Simplifying the equation, we get 24h+111=30324h + 111 = 303. Subtracting 111111 from both sides of the equation, we get 24h=303−11124h = 303 - 111, which simplifies to 24h=19224h = 192. We now divide both sides of the equation by 2424 to solve for hh. This gives us h=19224h = \frac{192}{24}, which simplifies to hh00.

More problems from Solve a system of equations using elimination: word problems

Question
Solve using substitution. 5x−2y=−7 5x - 2y = -7 x=−5 x = -5 (_,_)
Get tutor helpright-arrow

Posted 5 months ago

Question
Is (1,1)(1,1) a solution to this system of equations? \newline4x+10y=144x + 10y = 14\newlinex+6y=7x + 6y = 7\newlineChoices:\newline(A) yes \newline(B) no
Get tutor helpright-arrow

Posted 5 months ago

Question
Which describes the system of equations below?\newliney=–3x+9y = –3x + 9 \newliney=–3x+9y = –3x + 9 \newlineChoices:\newline(A) consistent and independent\text{(A) consistent and independent} \newline(B) consistent and dependent\text{(B) consistent and dependent} \newline(C) inconsistent\text{(C) inconsistent}
Get tutor helpright-arrow

Posted 5 months ago

Question
Solve using elimination. \newline7x−8y=−17 7x - 8y = -17 \newline −7x+3y=2 -7x + 3y = 2 \newline (____,____)(\_\_\_\_, \_\_\_\_)
Get tutor helpright-arrow

Posted 5 months ago

Question
Solve. \newlinex=−2 x = -2 \newline−2x+2y=−8 -2x + 2y = -8 \newline(____,____)(\_\_\_\_, \_\_\_\_)
Get tutor helpright-arrow

Posted 9 months ago

Question
Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.\newlineAt a community barbecue, Mrs. Wilkerson and Mr. Hogan are buying dinner for their families. Mrs. Wilkerson purchases 33 hot dog meals and 33 hamburger meals, paying a total of $36\$36. Mr. Hogan buys 11 hot dog meal and 33 hamburger meals, spending $26\$26 in all. How much do the meals cost?\newlineHot dog meals cost $\$_______ each, and hamburger meals cost $\$________ each.
Get tutor helpright-arrow

Posted 9 months ago

Question
Solve the system of equations by substitution.\newline−3x−y−3z=−11-3x - y - 3z = -11\newlinez=5z = 5\newlinex−y+3z=19x - y + 3z = 19\newline(____.____,____)
Get tutor helpright-arrow

Posted 5 months ago

Question
Solve the system of equations by elimination.\newlinex−3y−2z=10 x - 3y - 2z = 10 \newline3x+2y+2z=14 3x + 2y + 2z = 14 \newline2x−3y−2z=16 2x - 3y - 2z = 16 \newline(_,_,_)(\_,\_,\_)
Get tutor helpright-arrow

Posted 5 months ago

Question
Solve the system of equations.\newliney=x2+36x+3 y = x^2 + 36x + 3 \newliney=22x−37 y = 22x - 37 \newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(_,_)(\_,\_)\newline(_,_)(\_,\_)
Get tutor helpright-arrow

Posted 5 months ago

Question
Solve the system of equations.\newliney=−x−24 y = -x - 24 \newlinex2+y2=488 x^2 + y^2 = 488 \newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(_,_) (\_,\_) \newline(_,_) (\_,\_)
Get tutor helpright-arrow

Posted 5 months ago

View all (43)

Related topics

Algebra - Order of OperationsAlgebra - Distributive Property`X` and `Y` AxesGeometry - Scalene TriangleCommon MultipleGeometry - Quadrant