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 substitution, and fill in the blanks.\newlineDerek wants to make scrapbooks with old family photos. An online scrapbooking company charges $10\$10 for a basic book and $4\$4 per page. Meanwhile, a family friend is willing to make a scrapbook for $43\$43 plus $1\$1 per page. For a certain number of pages, the price would be equal. How much would that cost? How many pages would that be?\newlineThe scrapbook would cost $____\$\_\_\_\_ if it had ____\_\_\_\_ pages.

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Precalculusright chevron icon
Solve a system of equations using substitution: word problemsright chevron icon

Full solution

Q. Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.\newlineDerek wants to make scrapbooks with old family photos. An online scrapbooking company charges $10\$10 for a basic book and $4\$4 per page. Meanwhile, a family friend is willing to make a scrapbook for $43\$43 plus $1\$1 per page. For a certain number of pages, the price would be equal. How much would that cost? How many pages would that be?\newlineThe scrapbook would cost $____\$\_\_\_\_ if it had ____\_\_\_\_ pages.
  1. Define Variables: Let's define the variables.\newlineLet xx represent the number of pages in the scrapbook.\newlineLet yy represent the total cost of the scrapbook.
  2. Write Equations: Write the equations based on the given information.\newlineFor the online scrapbooking company: y=10+4xy = 10 + 4x (since the basic book is $10\$10 and each page is $4\$4).\newlineFor the family friend: y=43+xy = 43 + x (since the basic book is $43\$43 and each page is $1\$1).
  3. Set up System: Set up the system of equations.\newlineWe have two equations:\newline11) y=10+4xy = 10 + 4x\newline22) y=43+xy = 43 + x
  4. Solve by Substitution: Solve the system using substitution.\newlineSince both equations equal yy, we can set them equal to each other to find the value of xx:\newline10+4x=43+x10 + 4x = 43 + x
  5. Solve for x: Solve for x.\newlineSubtract xx from both sides:\newline10+4x−x=43+x−x10 + 4x - x = 43 + x - x\newline10+3x=4310 + 3x = 43
  6. Isolate Variable Term: Subtract 1010 from both sides to isolate the variable term.\newline3x=43−103x = 43 - 10\newline3x=333x = 33
  7. Calculate xx: Divide both sides by 33 to solve for xx.
    x=333x = \frac{33}{3}
    x=11x = 11
  8. Substitute xx: Substitute xx back into one of the original equations to find yy. Using the first equation: y=10+4xy = 10 + 4x y=10+4(11)y = 10 + 4(11)
  9. Calculate yy: Calculate the value of yy.y=10+44y = 10 + 44y=54y = 54
  10. Final Answer: Write the final answer.\newlineThe scrapbook would cost $54\$54 if it had 1111 pages.

More problems from Solve a system of equations using substitution: 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 (41)

Related topics

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