L14 · Problems with systems

1. 1.

   Adult tickets cost $8 and child tickets cost $6. 6 tickets cost $40. If 2 were adult tickets, how many were child tickets?

   Answer. 4

   2 adults + 4 children = 6 tickets, and 2(8) + 4(6) = 40.

2. 2.

   Adult tickets cost $14 and child tickets cost $6. 5 tickets cost $46. If 2 were adult tickets, how many were child tickets?

   Answer. 3

   2 adults + 3 children = 5 tickets, and 2(14) + 3(6) = 46.

3. 3.

   Adult tickets cost $14 and child tickets cost $4. 8 tickets cost $62. If 3 were adult tickets, how many were child tickets?

   Answer. 5

   3 adults + 5 children = 8 tickets, and 3(14) + 5(4) = 62.

4. 4.

   Adult tickets cost $11 and child tickets cost $4. 9 tickets cost $64. If 4 were adult tickets, how many were child tickets?

   Answer. 5

   4 adults + 5 children = 9 tickets, and 4(11) + 5(4) = 64.

5. 5.

   Adult tickets cost $10 and child tickets cost $6. 5 tickets cost $42. If 3 were adult tickets, how many were child tickets? Then Mei needs 3 of that amount. What is the total they need?

   Answer. 6

   3 adults + 2 children = 5 tickets, and 3(10) + 2(6) = 42. Then multiply by 3: 6.

6. 6.

   Adult tickets cost $11 and child tickets cost $7. 5 tickets cost $47. If 3 were adult tickets, how many were child tickets? Then Elena needs 2 of that amount. What is the total they need?

   Answer. 4

   3 adults + 2 children = 5 tickets, and 3(11) + 2(7) = 47. Then multiply by 2: 4.

7. 7.

   Adult tickets cost $10 and child tickets cost $6. 6 tickets cost $44. If 2 were adult tickets, how many were child tickets? Then Theo needs 4 of that amount. What is the total they need?

   Answer. 16

   2 adults + 4 children = 6 tickets, and 2(10) + 4(6) = 44. Then multiply by 4: 16.

8. 8.

   Adult tickets cost $14 and child tickets cost $5. 10 tickets cost $95. If 5 were adult tickets, how many were child tickets? Then Theo needs 3 of that amount. What is the total they need?

   Answer. 15

   5 adults + 5 children = 10 tickets, and 5(14) + 5(5) = 95. Then multiply by 3: 15.

9. 9.

   Adult tickets cost $11 and child tickets cost $6. 7 tickets cost $62. If 4 were adult tickets, how many were child tickets? Then Jonah needs 2 of that amount. What is the total they need?

   Answer. 6

   4 adults + 3 children = 7 tickets, and 4(11) + 3(6) = 62. Then multiply by 2: 6.

10. 10.

    Adult tickets cost $12 and child tickets cost $6. 9 tickets cost $72. If 3 were adult tickets, how many were child tickets? Then Ava needs 3 of that amount. What is the total they need?

    Answer. 18

    3 adults + 6 children = 9 tickets, and 3(12) + 6(6) = 72. Then multiply by 3: 18.

11. 11.

    Think

    Nora tried this problem:
    Adult tickets cost $10 and child tickets cost $7. 8 tickets cost $65. If 3 were adult tickets, how many were child tickets?
    Nora wrote 10. That is not correct. What is the right answer?

    Answer. 5

    Nora’s answer 10 is off. 3 adults + 5 children = 8 tickets, and 3(10) + 5(7) = 65.

12. 12.

    Think

    Ava tried this problem:
    Adult tickets cost $8 and child tickets cost $4. 7 tickets cost $40. If 3 were adult tickets, how many were child tickets?
    Ava wrote 8. That is not correct. What is the right answer?

    Answer. 4

    Ava’s answer 8 is off. 3 adults + 4 children = 7 tickets, and 3(8) + 4(4) = 40.

Original extra practice. Keys are computed from the items, not guessed.