Free printable Thanksgiving activity

Thanksgiving Algebra Meal Planning with Systems

A printable 20-problem Thanksgiving Algebra activity using meal planning, tickets, mixtures, budgets, and systems with solutions.

Grades 8–1020 problemsAbout 75 minutesReference data and answers
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Why this activity works

Systems become meaningful when two constraints must hold at once. Students model head counts, costs, mixtures, and capacity limits, then decide whether substitution, elimination, or graphing is the cleanest method.

Teaching note

A solution without defined variables is incomplete. Require students to state what x and y mean before writing equations and to check both original constraints afterward.

Materials

  • Pencil
  • Scratch paper
  • Optional graph paper

Directions

Define variables, write a system for every situation, solve using a suitable method, and interpret the ordered pair with units.

Complete activity preview

Use the reference table above when provided. All questions and solutions also appear in the printable packet.

Guest counts

Model totals and category differences with two equations.

  1. 1A dinner has 84 guests: adults and children. There are 18 more adults than children. Find each count.
  2. 2There are 46 tables, some seating 6 and some seating 8, with 320 seats total. Find each table count.
  3. 3A pantry has 70 boxes of rice and pasta. There are twice as many rice boxes as pasta boxes plus 4. Find each.
  4. 4A dinner has 96\displaystyle 96 guests. Adult groups seat 8\displaystyle 8 and youth groups seat 6\displaystyle 6. There are 14\displaystyle 14 groups. Find each type.
  5. 5Write a system for x\displaystyle x adult meals and y\displaystyle y child meals totaling 120\displaystyle 120, with 24\displaystyle 24 more adult meals.

Tickets and budgets

Use item counts and total revenue or cost.

  1. 6Adult tickets cost $12 and student tickets cost $7. Forty tickets bring in $390. Find each count.
  2. 7Large trays cost $35 and small trays cost $20. Ten trays cost $275. Find each count.
  3. 8A shopper buys 14 bags of rice and beans for $47. Rice costs $4 and beans $2.50. Find each count.
  4. 9Premium tickets cost $18\displaystyle 18 and standard tickets $11\displaystyle 11. A total of 52\displaystyle 52 tickets earns $712\displaystyle 712. Find each count.
  5. 10Write and solve a system for 16\displaystyle 16 trays costing $410\displaystyle 410 when large trays cost $35\displaystyle 35 and small trays $20\displaystyle 20.

Mixtures and rates

Model combined quantities with different concentrations or speeds.

  1. 11Mix nuts costing $3 per pound with nuts costing $7 per pound to make 20 pounds of a mixture worth $100. Find the amount of each type.
  2. 12A 30-liter drink is 40%\displaystyle 40\% juice using 25%\displaystyle 25\% and 55%\displaystyle 55\% mixtures. Find liters of each.
  3. 13Two packing lines together fill 54 boxes per hour. One fills 8 more than the other. Find each rate.
  4. 14Mix 20%\displaystyle 20\% and 50%\displaystyle 50\% solutions to make 24\displaystyle 24 liters of 35%\displaystyle 35\% solution. Find each amount.
  5. 15Two crews pack 180\displaystyle 180 boxes in 4\displaystyle 4 hours. One crew works 5\displaystyle 5 boxes per hour faster. Find their hourly rates.

Planning challenge

Analyze intersections and constraints in less direct models.

  1. 16Caterer A charges a $120 setup fee plus $4 per guest. Caterer B charges a $60 setup fee plus $7 per guest. For how many guests do the caterers charge the same total, and what is that total?
  2. 17A host makes 10 centerpieces. Each large centerpiece uses 3 pumpkins, and each small centerpiece uses 2 pumpkins. If the host uses 26 pumpkins, how many centerpieces of each size are there?
  3. 18A kitchen prepares 18 serving trays. Each large tray holds 4 servings, and each small tray holds 2 servings. The trays hold 52 servings altogether. How many trays of each size were prepared?
  4. 19A fundraiser sells 40 meal tickets. Adult tickets cost $13, and child tickets cost $8. If ticket sales total $440, how many tickets of each type were sold?
  5. 20A dinner serves 80 guests. Standard meals cost $12 each, and vegetarian meals cost $9 each. If the meals cost $870 altogether, how many of each meal were ordered?
Open the complete solutions

Equivalent forms and clearly supported open-ended responses should receive credit.

Guest counts

1. 51 adults and 33 children

2. 24 six-seat tables and 22 eight-seat tables

3. 48 rice and 22 pasta boxes

4. 6\displaystyle 6 adult groups and 8\displaystyle 8 youth groups

5. x+y=120\displaystyle x+y=120 and x−y=24\displaystyle x-y=24

Tickets and budgets

6. 22 adult and 18 student tickets

7. 5 large and 5 small trays

8. 8 rice bags and 6 bean bags

9. 20\displaystyle 20 premium and 32\displaystyle 32 standard tickets

10. L+s=16\displaystyle L+s=16, 35L+20s=410\displaystyle 35L+20s=410; L=6\displaystyle L=6, s=10\displaystyle s=10

Mixtures and rates

11. 10 pounds of each

12. 15 liters of each

13. 31 and 23 boxes per hour

14. 12\displaystyle 12 liters of each

15. 25\displaystyle 25 and 20\displaystyle 20 boxes per hour

Planning challenge

16. 20 guests; both caterers charge $200

17. 6 large centerpieces and 4 small centerpieces

18. 8 large trays and 10 small trays

19. 24 adult tickets and 16 child tickets

20. 50 standard meals and 30 vegetarian meals

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