{
  "problem": "All of the 5th grade teachers and students from Oak went on a field trip to an archaeology museum. Tickets were $$6.00$ each for teachers and $$2.50$ each for students, and the group paid $$35.50$ in total. The next month, the same group visited a natural history museum where the tickets cost $$24.00$ each for teachers and $$9.50$ each for students, and the group paid $$138.50$ in total. Find the number of teachers and students on the field trips.",
  "hints": [
    "Let",
    "$x$",
    "equal the number of teachers and",
    "$y$",
    "equal the number of students.",
    "The system of equations is:",
    "${6x+2.5y = 35.5}$",
    "${24x+9.5y = 138.5}$",
    "Solve for",
    "$x$",
    "and",
    "$y$",
    "using elimination.",
    "Multiply the top equation by",
    "$-4$",
    "${-24x-10y = -142}$",
    "${24x+9.5y = 138.5}$",
    "Add the top and bottom equations together.",
    "$ -0.5y = -3.5 $",
    "$ y = \\dfrac{-3.5}{-0.5}$",
    "${y = 7}$",
    "Now that you know",
    "${y = 7}$",
    ", plug it back into",
    "$ {6x+2.5y = 35.5}$",
    "to find",
    "$x$",
    "${6x + 2.5}{(7)}{= 35.5}$",
    "$6x+17.5 = 35.5$",
    "$6x = 18$",
    "$x = \\dfrac{18}{6}$",
    "${x = 3}$",
    "You can also plug",
    "${y = 7}$",
    "into",
    "$ {24x+9.5y = 138.5}$",
    "and get the same answer for",
    "$x$",
    "${24x + 9.5}{(7)}{= 138.5}$",
    "${x = 3}$",
    "There were $3$ teachers and $7$ students on the field trips."
  ]
}
{'source': 'AMPS', 'file': 'amps/khan/359/1608165960.json'}