Equations in x and y: write one for a story, and check a solution pair

Answer Key - Grade 9 Math Worksheet - Challenge Me

Circle the best answer, or write your answer on the line.

1. Read this first

   Use this

   Table of pairs (count | count). A pair fits the story when it solves the equation and both counts are whole numbers, zero or more.

2. 1.

   Tala buys c cookies at $2 and d drinks at $3 for $24, so 2c + 3d = 24. Which pair (c, d) makes sense in the story?

   • (4.5, 5)
   • (6, 4)
   • (12, 12)
   • (4, 6)
3. 2.

   Pia buys f fruit cups at $5 and w water bottles at $2 for $31, so 5f + 2w = 31. Which pair (f, w) makes sense in the story?

   • (5, 3)
   • (20, 11)
   • (3, 5)
   • (7, -2)
4. 3.

   Bo buys h hats at $4 and g games at $3 for $25, so 4h + 3g = 25. Which pair (h, g) makes sense in the story?

   • (3, 4)
   • (15, 10)
   • (4, 3)
   • (7, -1)
5. 4.

   The line is 2x + ky = 16. Milo knows the pair (3, 2) is a solution of 2x + ky = 16. What is k?

   5
6. 5.

   The line is 3x + ky = 26. Zee knows the pair (2, 4) is a solution of 3x + ky = 26. What is k?

   5
7. 6.

   The line is 4x + ky = 32. Ari knows the pair (2, 4) is a solution of 4x + ky = 32. What is k?

   6

8. Input–output table

   x	y
   0	9

   First rows.

   The rule is 3x + 5y = 45.

9. 7.

   Ren has 45 coins. A ride costs 3 coins and a game costs 5 coins. How many (rides, games) pairs of whole numbers use exactly 45 coins, with zero allowed?

   4

10. Input–output table

    x	y
    0	10

    First rows.

    The rule is 2x + 3y = 30.

11. 8.

    Noah packs 30 balloons. A small pack holds 2 and a big pack holds 3. How many (small, big) pairs of whole numbers hold exactly 30 balloons, with zero allowed?

    6
12. 9.

    Total 17. Ari buys c notebooks at $3 each and g pens at $2 each, and spends $17. If Ari buys 3 notebooks, how many pens is that?

    4
13. 10.

    Total 29. Luz buys d binders at $4 each and f folders at $3 each, and spends $29. If Luz buys 2 binders, how many folders is that?

    7