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Systems of Inequalities Word Problems: Does It Meet Both Constraints? — Easy Worksheet 2
Grade 9 · Whoobee Name: ____________________ Date: __________
Answer yes or no. Substitute the numbers into both inequalities; the choice works only if both are true.
How to solve
Put the numbers into each inequality. Work out the cost (price × number, then add) and the total count. "At least" means ≥ and "at most" means ≤, so hitting the limit exactly still counts. The answer is yes only if both inequalities are true.
Example
Lily has at most $19.00 to spend on school supplies. Lily can choose notebooks, n, at $2.00 each, and pens, p, at $0.75 each. Lily needs at least 13 items. Lily wrote the inequalities 2.00n + 0.75p ≤ 19 and n + p ≥ 13. If Lily buys 7 notebooks and 6 pens, will this satisfy both constraints? Answer yes or no.
Answer: yes
Not quite. The answer is
💡 Substitute a = 29 and s = 4. Money: 9.00(29) + 4.50(4) = 261.00 + 18.00 = 279.00, and 279.00 ≥ 279 is true. Count: 29 + 4 = 33, and 33 ≤ 36 is true. Both are true, so yes, this choice satisfies both constraints.
✓ Correct!
Not quite. The answer is
💡 Substitute a = 29 and s = 4. Money: 9.00(29) + 4.50(4) = 261.00 + 18.00 = 279.00, and 279.00 ≥ 279 is true. Count: 29 + 4 = 33, and 33 ≤ 36 is true. Both are true, so yes, this choice satisfies both constraints.
💡 How to solve: Systems of Inequalities Word Problems: Does It Meet Both Constraints?
Put the numbers into each inequality. Work out the cost (price × number, then add) and the total count. "At least" means ≥ and "at most" means ≤, so hitting the limit exactly still counts. The answer is yes only if both inequalities are true.
Try a similar one
Leo has at most $26.00 to spend on school supplies. Leo can choose notebooks, n, at $2.75 each, and pens, p, at $1.00 each. Leo needs at least 12 items. Leo wrote the inequalities 2.75n + 1.00p ≤ 26 and n + p ≥ 12. If Leo buys 5 notebooks and 9 pens, will this satisfy both constraints? Answer yes or no.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Substitute m = 5 and c = 3. Money: 2.75(5) + 1.00(3) = 13.75 + 3.00 = 16.75, and 16.75 ≤ 28 is true. Count: 5 + 3 = 8, and 8 ≥ 11 is false. Both must be true, so no, this choice does not satisfy both constraints.
✓ Correct!
Not quite. The answer is
💡 Substitute m = 5 and c = 3. Money: 2.75(5) + 1.00(3) = 13.75 + 3.00 = 16.75, and 16.75 ≤ 28 is true. Count: 5 + 3 = 8, and 8 ≥ 11 is false. Both must be true, so no, this choice does not satisfy both constraints.
💡 How to solve: Systems of Inequalities Word Problems: Does It Meet Both Constraints?
Put the numbers into each inequality. Work out the cost (price × number, then add) and the total count. "At least" means ≥ and "at most" means ≤, so hitting the limit exactly still counts. The answer is yes only if both inequalities are true.
Try a similar one
Emma needs to raise at least $412.00 selling tickets for the school play. Emma can choose adult tickets, a, at $10.00 each, and student tickets, s, at $5.50 each. There are at most 44 seats, so Emma can sell at most 44 tickets. Emma wrote the inequalities 10.00a + 5.50s ≥ 412 and a + s ≤ 44. If Emma sells 41 adult tickets and 3 student tickets, will this satisfy both constraints? Answer yes or no.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Substitute m = 11 and c = 1. Money: 2.75(11) + 0.75(1) = 30.25 + 0.75 = 31.00, and 31.00 ≤ 31 is true. Count: 11 + 1 = 12, and 12 ≥ 12 is true. Both are true, so yes, this choice satisfies both constraints.
✓ Correct!
Not quite. The answer is
💡 Substitute m = 11 and c = 1. Money: 2.75(11) + 0.75(1) = 30.25 + 0.75 = 31.00, and 31.00 ≤ 31 is true. Count: 11 + 1 = 12, and 12 ≥ 12 is true. Both are true, so yes, this choice satisfies both constraints.
💡 How to solve: Systems of Inequalities Word Problems: Does It Meet Both Constraints?
Put the numbers into each inequality. Work out the cost (price × number, then add) and the total count. "At least" means ≥ and "at most" means ≤, so hitting the limit exactly still counts. The answer is yes only if both inequalities are true.
Try a similar one
Zara has at most $29.00 to spend on school supplies. Zara can choose notebooks, n, at $2.75 each, and pens, p, at $0.75 each. Zara needs at least 11 items. Zara wrote the inequalities 2.75n + 0.75p ≤ 29 and n + p ≥ 11. If Zara buys 7 notebooks and 8 pens, will this satisfy both constraints? Answer yes or no.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Substitute m = 2 and c = 6. Money: 3.00(2) + 0.75(6) = 6.00 + 4.50 = 10.50, and 10.50 ≤ 15 is true. Count: 2 + 6 = 8, and 8 ≥ 10 is false. Both must be true, so no, this choice does not satisfy both constraints.
✓ Correct!
Not quite. The answer is
💡 Substitute m = 2 and c = 6. Money: 3.00(2) + 0.75(6) = 6.00 + 4.50 = 10.50, and 10.50 ≤ 15 is true. Count: 2 + 6 = 8, and 8 ≥ 10 is false. Both must be true, so no, this choice does not satisfy both constraints.
💡 How to solve: Systems of Inequalities Word Problems: Does It Meet Both Constraints?
Put the numbers into each inequality. Work out the cost (price × number, then add) and the total count. "At least" means ≥ and "at most" means ≤, so hitting the limit exactly still counts. The answer is yes only if both inequalities are true.
Try a similar one
Maya has at most $14.00 to spend on school supplies. Maya can choose notebooks, n, at $1.50 each, and pens, p, at $1.00 each. Maya needs at least 10 items. Maya wrote the inequalities 1.50n + 1.00p ≤ 14 and n + p ≥ 10. If Maya buys 4 notebooks and 6 pens, will this satisfy both constraints? Answer yes or no.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Substitute a = 11 and g = 1. Money: 0.50(11) + 1.50(1) = 5.50 + 1.50 = 7.00, and 7.00 ≤ 10 is true. Count: 11 + 1 = 12, and 12 ≥ 12 is true. Both are true, so yes, this choice satisfies both constraints.
✓ Correct!
Not quite. The answer is
💡 Substitute a = 11 and g = 1. Money: 0.50(11) + 1.50(1) = 5.50 + 1.50 = 7.00, and 7.00 ≤ 10 is true. Count: 11 + 1 = 12, and 12 ≥ 12 is true. Both are true, so yes, this choice satisfies both constraints.
💡 How to solve: Systems of Inequalities Word Problems: Does It Meet Both Constraints?
Put the numbers into each inequality. Work out the cost (price × number, then add) and the total count. "At least" means ≥ and "at most" means ≤, so hitting the limit exactly still counts. The answer is yes only if both inequalities are true.
Try a similar one
Arman can spend at most $20.00 on treats for a bake sale. Arman can choose muffins, m, at $2.00 each, and cookies, c, at $1.00 each. Arman needs at least 13 treats. Arman wrote the inequalities 2.00m + 1.00c ≤ 20 and m + c ≥ 13. If Arman buys 1 muffin and 14 cookies, will this satisfy both constraints? Answer yes or no.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Substitute a = 30 and s = 25. Money: 9.50(30) + 5.50(25) = 285.00 + 137.50 = 422.50, and 422.50 ≥ 466 is false. Count: 30 + 25 = 55, and 55 ≤ 56 is true. Both must be true, so no, this choice does not satisfy both constraints.
✓ Correct!
Not quite. The answer is
💡 Substitute a = 30 and s = 25. Money: 9.50(30) + 5.50(25) = 285.00 + 137.50 = 422.50, and 422.50 ≥ 466 is false. Count: 30 + 25 = 55, and 55 ≤ 56 is true. Both must be true, so no, this choice does not satisfy both constraints.
💡 How to solve: Systems of Inequalities Word Problems: Does It Meet Both Constraints?
Put the numbers into each inequality. Work out the cost (price × number, then add) and the total count. "At least" means ≥ and "at most" means ≤, so hitting the limit exactly still counts. The answer is yes only if both inequalities are true.
Try a similar one
It costs Ani at least $4.00 to mail a package. Ani can choose postcard stamps, p, at $0.25 each, and first-class stamps, f, at $0.50 each. Ani can fit at most 9 stamps on the package. Ani wrote the inequalities 0.25p + 0.50f ≥ 4 and p + f ≤ 9. If Ani uses 1 postcard stamp and 8 first-class stamps, will this satisfy both constraints? Answer yes or no.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Substitute p = 4 and f = 6. Money: 0.25(4) + 0.50(6) = 1.00 + 3.00 = 4.00, and 4.00 ≥ 4 is true. Count: 4 + 6 = 10, and 10 ≤ 10 is true. Both are true, so yes, this choice satisfies both constraints.
✓ Correct!
Not quite. The answer is
💡 Substitute p = 4 and f = 6. Money: 0.25(4) + 0.50(6) = 1.00 + 3.00 = 4.00, and 4.00 ≥ 4 is true. Count: 4 + 6 = 10, and 10 ≤ 10 is true. Both are true, so yes, this choice satisfies both constraints.
💡 How to solve: Systems of Inequalities Word Problems: Does It Meet Both Constraints?
Put the numbers into each inequality. Work out the cost (price × number, then add) and the total count. "At least" means ≥ and "at most" means ≤, so hitting the limit exactly still counts. The answer is yes only if both inequalities are true.
Try a similar one
Lily has $23.00 to spend on snacks for a class trip. Lily can choose apples, a, at $0.50 each, and granola bars, g, at $1.50 each. Lily needs at least 17 snacks. Lily wrote the inequalities 0.50a + 1.50g ≤ 23 and a + g ≥ 17. If Lily buys 18 apples and 3 granola bars, will this satisfy both constraints? Answer yes or no.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Substitute b = 6 and m = 6. Money: 12.50(6) + 11.25(6) = 75.00 + 67.50 = 142.50, and 142.50 ≥ 105 is true. Count: 6 + 6 = 12, and 12 ≤ 10 is false. Both must be true, so no, this choice does not satisfy both constraints.
✓ Correct!
Not quite. The answer is
💡 Substitute b = 6 and m = 6. Money: 12.50(6) + 11.25(6) = 75.00 + 67.50 = 142.50, and 142.50 ≥ 105 is true. Count: 6 + 6 = 12, and 12 ≤ 10 is false. Both must be true, so no, this choice does not satisfy both constraints.
💡 How to solve: Systems of Inequalities Word Problems: Does It Meet Both Constraints?
Put the numbers into each inequality. Work out the cost (price × number, then add) and the total count. "At least" means ≥ and "at most" means ≤, so hitting the limit exactly still counts. The answer is yes only if both inequalities are true.
Try a similar one
Zara has at most $17.00 to spend on school supplies. Zara can choose notebooks, n, at $2.00 each, and pens, p, at $0.75 each. Zara needs at least 14 items. Zara wrote the inequalities 2.00n + 0.75p ≤ 17 and n + p ≥ 14. If Zara buys 2 notebooks and 15 pens, will this satisfy both constraints? Answer yes or no.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
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Systems of Inequalities Word Problems: Does It Meet Both Constraints? — Easy Worksheet 2
Answer yes or no. Substitute the numbers into both inequalities; the choice works only if both are true.