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 any method, and fill in the blanks.\newlineA baseball coach takes her team out for pizza every time they win a game. Not everyone can come each time, so she orders the pizzas based on how many players are coming. After last week's victory, she bought 33 small pizzas and 22 large pizzas, the perfect amount for the 1414 players going out for pizza. This week, there were 1212 players going, so she ordered 22 small pizzas and 22 large pizzas, which was also the right amount. How many people does each size of pizza feed?\newlineEach small pizza feeds _\_ people, and each large pizza feeds _\_ people.

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 any method: word problemsright chevron icon

Full solution

Q. Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.\newlineA baseball coach takes her team out for pizza every time they win a game. Not everyone can come each time, so she orders the pizzas based on how many players are coming. After last week's victory, she bought 33 small pizzas and 22 large pizzas, the perfect amount for the 1414 players going out for pizza. This week, there were 1212 players going, so she ordered 22 small pizzas and 22 large pizzas, which was also the right amount. How many people does each size of pizza feed?\newlineEach small pizza feeds _\_ people, and each large pizza feeds _\_ people.
  1. Define Variables: Let's denote the number of people a small pizza can feed as xx and the number of people a large pizza can feed as yy. After last week's victory, the coach bought 33 small pizzas and 22 large pizzas for 1414 players. This gives us our first equation:\newline3x+2y=143x + 2y = 14
  2. First Equation: This week, there were 1212 players going, and the coach ordered 22 small pizzas and 22 large pizzas. This gives us our second equation:\newline2x+2y=122x + 2y = 12
  3. Second Equation: We now have a system of equations:\newline3x+2y=143x + 2y = 14\newline2x+2y=122x + 2y = 12\newlineWe can solve this system by subtracting the second equation from the first to eliminate yy.\newline(3x+2y)−(2x+2y)=14−12(3x + 2y) - (2x + 2y) = 14 - 12\newline3x−2x+2y−2y=23x - 2x + 2y - 2y = 2\newlinex=2x = 2
  4. Solve System of Equations: Now that we have the value for xx, we can substitute it back into one of the original equations to solve for yy. Let's use the second equation:\newline2(2)+2y=122(2) + 2y = 12\newline4+2y=124 + 2y = 12\newline2y=12−42y = 12 - 4\newline2y=82y = 8\newliney=4y = 4
  5. Substitute and Solve for xx: We have found the values for xx and yy:x=2x = 2y=4y = 4This means each small pizza feeds 22 people, and each large pizza feeds 44 people.

More problems from Solve a system of equations using any method: 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 (92)

Related topics

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