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.\newlineScouting troops in Carroll County are putting on a crab feed to raise money for camp. They offer a complete crab dinner as well as a vegetarian option. One troop member sold tickets for 1818 crab meals and 3838 vegetarian meals, with total receipts of $1,546\$1,546. Another sold tickets for 3030 crab meals and 3030 vegetarian meals, bringing in a total of $1,710\$1,710. How much do the two types of tickets cost?\newlineA ticket for a crab meal costs $____\$\_\_\_\_, and a ticket for a vegetarian meal costs $____\$\_\_\_\_.

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 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.\newlineScouting troops in Carroll County are putting on a crab feed to raise money for camp. They offer a complete crab dinner as well as a vegetarian option. One troop member sold tickets for 1818 crab meals and 3838 vegetarian meals, with total receipts of $1,546\$1,546. Another sold tickets for 3030 crab meals and 3030 vegetarian meals, bringing in a total of $1,710\$1,710. How much do the two types of tickets cost?\newlineA ticket for a crab meal costs $____\$\_\_\_\_, and a ticket for a vegetarian meal costs $____\$\_\_\_\_.
  1. Define variables: Let's define the variables: Let xx be the price of a crab meal ticket, and yy be the price of a vegetarian meal ticket.
  2. Write equations: Write the equations based on the information given: \newline11st troop member: 18x+38y=154618x + 38y = 1546 \newline22nd troop member: 30x+30y=171030x + 30y = 1710
  3. Multiply and align coefficients: Multiply the first equation by 3030 and the second by 1818 to align the coefficients for elimination:\newline11st equation: 540x+1140y=46380540x + 1140y = 46380\newline22nd equation: 540x+540y=30780540x + 540y = 30780
  4. Eliminate xx: Subtract the second equation from the first to eliminate xx:540x+1140y−(540x+540y)=46380−30780540x + 1140y - (540x + 540y) = 46380 - 30780600y=15600600y = 15600
  5. Solve for y: Solve for y:\newliney=15600600y = \frac{15600}{600}\newliney=26y = 26
  6. Substitute and find xx: Substitute y=26y = 26 back into the second original equation to find xx:30x+30(26)=171030x + 30(26) = 171030x+780=171030x + 780 = 1710
  7. Solve for x: Solve for x:\newline30x=1710−78030x = 1710 - 780\newline30x=93030x = 930\newlinex=93030x = \frac{930}{30}\newlinex=31x = 31

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 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 (31)

Related topics

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