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.\newlineTwo classmates got together over the weekend to do their assigned History reading. Leo can read 11 page per minute, while Shawna can read 33 pages per minute. When they met, Leo had already read 7575 pages, and Shawna had already gotten through 1919 pages. After a while, they had both read the same number of pages. How many pages had each one read? How long did that take?\newlineLeo and Shawna had each read _\_ pages after _\_ minutes.

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Grade 8right 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.\newlineTwo classmates got together over the weekend to do their assigned History reading. Leo can read 11 page per minute, while Shawna can read 33 pages per minute. When they met, Leo had already read 7575 pages, and Shawna had already gotten through 1919 pages. After a while, they had both read the same number of pages. How many pages had each one read? How long did that take?\newlineLeo and Shawna had each read _\_ pages after _\_ minutes.
  1. Define Variables: Let's define the variables:\newlineLet xx be the number of minutes they read together.\newlineLet LL be the total number of pages Leo read.\newlineLet SS be the total number of pages Shawna read.\newlineWe can write two equations based on the given information:\newlineFor Leo: L=75+1×xL = 75 + 1 \times x (since Leo reads 11 page per minute and had already read 7575 pages)\newlineFor Shawna: S=19+3×xS = 19 + 3 \times x (since Shawna reads 33 pages per minute and had already read 1919 pages)\newlineWe are also told that after a while, they had both read the same number of pages, which gives us the equation:\newlineL=SL = S
  2. Write Equations: Now we can set up the system of equations:\newline11. L=75+xL = 75 + x\newline22. S=19+3xS = 19 + 3x\newlineAnd since L=SL = S, we can substitute the expression for LL from the first equation into the second equation:\newline75+x=19+3x75 + x = 19 + 3x
  3. Set Up System: Next, we solve for xx:75+x=19+3x75 + x = 19 + 3xSubtract xx from both sides:75=19+2x75 = 19 + 2xSubtract 1919 from both sides:56=2x56 = 2xDivide both sides by 22:x=28x = 28
  4. Solve for x: Now that we have the value of xx, we can find the total number of pages each person read. We'll substitute xx back into the equations for LL and SS:
    For Leo: L=75+x=75+28=103L = 75 + x = 75 + 28 = 103 pages
    For Shawna: S=19+3x=19+3×28=19+84=103S = 19 + 3x = 19 + 3\times28 = 19 + 84 = 103 pages
  5. Find Total Pages: We have found that both Leo and Shawna read 103103 pages each after 2828 minutes.

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 8 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 8 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 (22)

Related topics

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