1. Let p = number of pigs, c = number of chickens.
Equations: p + c = 30, 4p + 2c = 84
Solve: Multiply first equation by 2 → 2p + 2c = 60; subtract from second: 2p = 24 → p = 12, c = 18
Answer: 12 pigs, 18 chickens
2. Let s = small drinks, l = large drinks.
Equations: s + l = 59, 1.75s + 2.25l = 118.75
Solve: Multiply first by 1.75 → 1.75s + 1.75l = 103.25; subtract from second: 0.5l = 15.5 → l = 31, s = 28
Answer: 28 small drinks, 31 large drinks
3. Let t = tacos, b = burritos.
Equations: t + b = 50, 1.50t + 2.00b = 88.50
Solve: Multiply first by 1.50 → 1.50t + 1.50b = 75; subtract from second: 0.50b = 13.50 → b = 27, t = 23
Answer: 23 tacos, 27 burritos
4. Let a = apple pies, c = cherry pies.
Equations: a + c = 20, 1.40a + 1.80c = 31.40
Solve: Multiply first by 1.40 → 1.40a + 1.40c = 28; subtract from second: 0.40c = 3.40 → c = 8.5 → not integer → error in problem or data
Recheck: If total sold is 20, and total revenue $31.40, then solving gives non-integer → likely typo; assuming correct values, no solution with whole pies.
5. Let f = football tickets, b = basketball tickets.
Equations: f + b = 25, 10f + 8b = 212
Solve: Multiply first by 8 → 8f + 8b = 200; subtract from second: 2f = 12 → f = 6, b = 19
Answer: 6 football tickets, 19 basketball tickets
6. Let w = white bikes, b = blue bikes.
Equations: w + b = 24, 12w + 15b = 288
Solve: Multiply first by 12 → 12w + 12b = 288; subtract from second: 3b = 0 → b = 0, w = 24
Answer: 24 white bikes, 0 blue bikes
7. Let s = student tickets, a = adult tickets.
Equations: s + a = 20, 3.50s + 5.00a = 84.50
Solve: Multiply first by 3.50 → 3.50s + 3.50a = 70; subtract from second: 1.50a = 14.50 → a = 9.666… → not integer → error in problem or data
Recheck: Likely typo; if total revenue is $85.50, then 1.50a = 15.50 → still not integer. If revenue is $84.00, then 1.50a = 14 → a=9.333… → no clean solution. Probably intended different numbers.
8. Let s = small pizzas, l = large pizzas.
Equations: s + l = 22, 8s + 12l = 208
Solve: Multiply first by 8 → 8s + 8l = 176; subtract from second: 4l = 32 → l = 8, s = 14
Answer: 14 small pizzas, 8 large pizzas
9. Let s = salami sandwiches, h = ham sandwiches.
Equations: s + h = 35, 1.25s + 1.50h = 47.50
Solve: Multiply first by 1.25 → 1.25s + 1.25h = 43.75; subtract from second: 0.25h = 3.75 → h = 15, s = 20
Answer: 20 salami sandwiches, 15 ham sandwiches
10. Let s = small sodas, l = large sodas.
Equations: s + l = 19, 1.25s + 1.75l = 28.75
Solve: Multiply first by 1.25 → 1.25s + 1.25l = 23.75; subtract from second: 0.50l = 5 → l = 10, s = 9
Answer: 9 small sodas, 10 large sodas
Parent Tip: Review the logic above to help your child master the concept of linear system word problems worksheet.
