Substitution and Elimination Word Problems

Homer sells tickets for admission to your school play and collects a total of $104. Admission prices are $6 for adults and $4 for children. He sold 21 tickets total. Solve the system:
x + y = 21
6x + 4y = 104

• (10, 11)

• (12, 9)

• (11, 10)

• (9, 12)

On Monday Joe bought 10 cups of coffee and 5 doughnuts for his office at the cost of $16.50. On Tuesday he bought 5 cups of coffee and 10 doughnuts for a total of $14.25. Which equations could be used to determine the cost of the coffee?

• 10c + 5d = 14.25
  5c + 10d = 16.50

• 10c + 5d = 16.50
  5c + 10d = 14.25

• c + d = 10
  5c + 10d = 16.50

• c + d = 5
  5c + 10d = 16.50

Your family goes to a restaurant for dinner. There are 6 people in your family. Some order the chicken dinner for $14.80, and some order steak for $17. If the total bill was $91, which system best represents the situation? 

• x + y = 6
  14.80x + 17y = 91

• x + y = 91
  14.80x + 17y = 6

• x + y = 6
  14.80y + 17x = 91

• x + y = 91
  14.80x+ 17y = 6

Flagship Cinemas sells movie tickets that are $4 for matinees and $7 for regular. One night, the theater sells 578 tickets and collects $3365 in total ticket sales.
Which system best represents the situation?

• 4x + 7y = 578
  x + y = 3365

• 4x + 7y = 3365
  x + y = 578

• 4y + 7x = 578
  x + y = 3365

• 4y + 7x = 3365
  x + y = 578

Which method would be most efficient to solve this system? Elimination or Substitution? Explain. (¿Qué método sería más eficaz para resolver este sistema? Eliminación o sustitución. Explique.)

Define the variables for this systems word problem. (Defina las variables para este problema de palabras del sistema.)

• x - # of multiple choice questions & y - # of word problems//x - # de preguntas de elección múltiple e y - # de problemas de palabras

• x - 1 point and y - 5 points//x - 1 puntos e y - 5 puntos

• x - 40 questions & y - 100 points//x - 40 preguntas e y - 100 puntos

Write the system of equations for this problem. (Escriba el sistema de ecuaciones para este problema.)

• x+y = 100 and 2x+4y = 30

• x+y = 30 and 2x+4y = 100

• x+y = 30 and x+4y = 100

• 4x+4y = 40 and x+y = 100

Which method would be most efficient to solve this system? Elimination or Substitution? Explain. (¿Qué método sería más eficaz para resolver este sistema? Eliminación o sustitución. Explique.)

Which method would be best (quickest) for solving the system below: x + y = 11 3x - 4y = -2

• Substitution

• Elimination

• Graphing

• None of these

Gabby and Sydney bought some pens and pencils. Gabby bought 4 pens and 5 pencils for $6.71. Sydney bought 5 pens and 3 pencils for $7.12. Find the cost of each.

• The cost of a pen is $1.19 and the cost of a pencil is $0.39.

• The cost of a pencil is $1.19 and the cost of a pen is $0.39.

• The cost of a pen is $6.71 and the cost of a pencil is $7.12.

• The cost of a pen is $7.12 and the cost of a pencil is $6.71.