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.\newlineEmily owns a cake shop and she is working on two wedding cakes this week. The first cake consists of 44 small tiers and 44 large tiers, which will serve a total of 268268 guests. The second one includes 22 small tiers and 44 large tiers, which is enough servings for 228228 guests. How many guests does each size of tier serve?\newlineA small tier will serve _\_ guests and a large tier will serve _\_ guests.

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.\newlineEmily owns a cake shop and she is working on two wedding cakes this week. The first cake consists of 44 small tiers and 44 large tiers, which will serve a total of 268268 guests. The second one includes 22 small tiers and 44 large tiers, which is enough servings for 228228 guests. How many guests does each size of tier serve?\newlineA small tier will serve _\_ guests and a large tier will serve _\_ guests.
  1. Equation for first cake: Let's denote the number of guests served by a small tier as ss and by a large tier as ll. The first cake, serving 268268 guests, consists of 44 small tiers and 44 large tiers, leading to the equation 4s+4l=2684s + 4l = 268.
  2. Equation for second cake: The second cake serves 228228 guests with 22 small tiers and 44 large tiers, giving us the equation 2s+4l=2282s + 4l = 228.
  3. Eliminating variable ss: To eliminate one variable, we'll focus on eliminating ss. Multiply the second equation by 22 to align the coefficients of ss with the first equation: 4s+8l=4564s + 8l = 456.
  4. Subtracting equations: Subtract the first equation from the modified second equation: 4s+8l)−(4s+4l)=456−268 simplifyingto$4l=1884s + 8l) - (4s + 4l) = 456 - 268\, simplifying to \$4l = 188.
  5. Solving for l: Solve for ll: l=1884l = \frac{188}{4}, which equals 4747.
  6. Substitute ll into first equation: Substitute l=47l = 47 back into the first equation: 4s+4×47=2684s + 4\times47 = 268. This simplifies to 4s+188=2684s + 188 = 268.
  7. Solving for s: Solve for s: 4s=268−1884s = 268 - 188, which simplifies to 4s=804s = 80. Then, s=804s = \frac{80}{4}, which equals 2020.

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