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. Maria has two reusable water bottles: a small one and a large one. Yesterday, she drank 44 small bottles and 33 large bottles, for a total of 3,0303,030 grams. The day before, she drank 22 small bottles and 33 large bottles, for a total of 2,2622,262 grams. How much does each bottle hold?\newlineThe small bottle holds _\_ grams and the large one holds _\_ grams.

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. Maria has two reusable water bottles: a small one and a large one. Yesterday, she drank 44 small bottles and 33 large bottles, for a total of 3,0303,030 grams. The day before, she drank 22 small bottles and 33 large bottles, for a total of 2,2622,262 grams. How much does each bottle hold?\newlineThe small bottle holds _\_ grams and the large one holds _\_ grams.
  1. Set up equations: Let's denote the small bottle's capacity as SS grams and the large bottle's capacity as LL grams. We can set up two equations based on the given information:\newlineFor the first day: 4S+3L=3,0304S + 3L = 3,030 grams\newlineFor the second day: 2S+3L=2,2622S + 3L = 2,262 grams
  2. Elimination method: To solve using elimination, we need to eliminate one of the variables. We can do this by multiplying the second equation by 22, so that the coefficient of SS in both equations is the same:\newlineFirst equation: 4S+3L=3,0304S + 3L = 3,030\newlineSecond equation (multiplied by 22): 4S+6L=4,5244S + 6L = 4,524
  3. Subtract and solve: Now, we subtract the second equation from the first equation to eliminate SS:(4S+3L)−(4S+6L)=3,030−4,524(4S + 3L) - (4S + 6L) = 3,030 - 4,524This simplifies to:−3L=−1,494-3L = -1,494
  4. Solve for L: We divide both sides by −3-3 to solve for LL:L=−1,494−3L = \frac{-1,494}{-3}L=498L = 498So, the large bottle holds 498498 grams.
  5. Substitute and solve: Now that we have the value for LL, we can substitute it back into one of the original equations to solve for SS. We'll use the second equation:\newline2S+3(498)=2,2622S + 3(498) = 2,262\newline2S+1,494=2,2622S + 1,494 = 2,262\newline2S=2,262−1,4942S = 2,262 - 1,494\newline2S=7682S = 768
  6. Final solution: Finally, we divide both sides by 22 to solve for SS:S=7682S = \frac{768}{2}S=384S = 384So, the small bottle holds 384384 grams.

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