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.\newlineStudents in a health class are tracking how much water they consume each day. Alexandra has two reusable water bottles: a small one and a large one. Yesterday, she drank 22 small bottles and 22 large bottles, for a total of 6464 ounces. The day before, she drank 11 small bottle and 22 large bottles, for a total of 5151 ounces. How much does each bottle hold?\newlineThe small bottle holds _____ ounces and the large one holds _____ ounces.

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 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.\newlineStudents in a health class are tracking how much water they consume each day. Alexandra has two reusable water bottles: a small one and a large one. Yesterday, she drank 22 small bottles and 22 large bottles, for a total of 6464 ounces. The day before, she drank 11 small bottle and 22 large bottles, for a total of 5151 ounces. How much does each bottle hold?\newlineThe small bottle holds _____ ounces and the large one holds _____ ounces.
  1. Define Variables: Let's define two variables: let xx be the number of ounces the small bottle holds, and yy be the number of ounces the large bottle holds. We can then write two equations based on the information given:\newline11. For the first day: 2x+2y=642x + 2y = 64 (since Alexandra drank 22 small and 22 large bottles)\newline22. For the second day: x+2y=51x + 2y = 51 (since she drank 11 small and 22 large bottles)
  2. Write Equations: To solve this system using elimination, we can multiply the second equation by 22 to align the coefficients of yy: \newline2(x+2y)=2(51)2(x + 2y) = 2(51)\newlineThis gives us a new equation:\newline2x+4y=1022x + 4y = 102
  3. Multiply Second Equation: Now we have two equations with the same coefficient for yy:1.2x+2y=641. 2x + 2y = 642.2x+4y=1022. 2x + 4y = 102We can subtract the first equation from the second to eliminate xx:(2x+4y)−(2x+2y)=102−64(2x + 4y) - (2x + 2y) = 102 - 64This simplifies to:2y=382y = 38
  4. Eliminate xx: Divide both sides of the equation by 22 to solve for yy:2y2=382\frac{2y}{2} = \frac{38}{2}y=19y = 19So, the large bottle holds 1919 ounces.
  5. Solve for y: Now that we know the value of yy, we can substitute it back into one of the original equations to solve for xx. Let's use the second equation:\newlinex+2(19)=51x + 2(19) = 51\newlinex+38=51x + 38 = 51
  6. Substitute Back: Subtract 3838 from both sides to solve for xx:\newlinex+38−38=51−38x + 38 - 38 = 51 - 38\newlinex=13x = 13\newlineSo, the small bottle holds 1313 ounces.

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 (28)

Related topics

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