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Word Problems — Easy Worksheet 2
Grade 12 · MathSheets Name: ____________________ Date: __________
Read each problem and solve.
How to solve
For rows that grow by the same amount, use the arithmetic sequence formula aₙ = a₁ + (n - 1)d. For a function model like P(m), substitute the given number for m and simplify.
Example
Rae saves $21 the first week and $4 more each week than the week before. How much has she saved in total after 8 weeks?
Answer: 280
Not quite. The answer is
💡 Each week she saves the same amount more, so the weekly savings form an arithmetic series. Use S_n = n2 × (2a_1 + (n − 1)d) with n = 6, a_1 = 11 and d = 3: S_6 = 62 × (2 × 11 + (6 − 1) × 3) = 62 × (22 + 15) = 62 × 37 = 111. She has saved $111 in total.
✓ Correct!
Not quite. The answer is
💡 Each week she saves the same amount more, so the weekly savings form an arithmetic series. Use S_n = n2 × (2a_1 + (n − 1)d) with n = 6, a_1 = 11 and d = 3: S_6 = 62 × (2 × 11 + (6 − 1) × 3) = 62 × (22 + 15) = 62 × 37 = 111. She has saved $111 in total.
💡 How to solve: Word Problems
For rows that grow by the same amount, use the arithmetic sequence formula aₙ = a₁ + (n - 1)d. For a function model like P(m), substitute the given number for m and simplify.
Try a similar one
Rae saves $29 the first week and $5 more each week than the week before. How much has she saved in total after 5 weeks?
✓ 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
💡 Set the cost equal to the bill and solve for g: 15g + 8 = 23. Subtract 8 from both sides: 15g = 15. Divide both sides by 15: g = 1. Check: 15 × 1 + 8 = 23. The plan used 1 gigabytes.
✓ Correct!
Not quite. The answer is
💡 Set the cost equal to the bill and solve for g: 15g + 8 = 23. Subtract 8 from both sides: 15g = 15. Divide both sides by 15: g = 1. Check: 15 × 1 + 8 = 23. The plan used 1 gigabytes.
💡 How to solve: Word Problems
For rows that grow by the same amount, use the arithmetic sequence formula aₙ = a₁ + (n - 1)d. For a function model like P(m), substitute the given number for m and simplify.
Try a similar one
Cans are stacked in a triangle: 1 can on top, 2 in the next row, 3 in the next, and so on. How many cans are in a stack with 5 rows?
✓ 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
💡 Each bounce multiplies the height by 12, so this is a geometric sequence: bounce n reaches 4 × (12)n. Bounce 2: 4 × (12)2 = 44 = 1 feet. The ball goes 1 feet high.
✓ Correct!
Not quite. The answer is
💡 Each bounce multiplies the height by 12, so this is a geometric sequence: bounce n reaches 4 × (12)n. Bounce 2: 4 × (12)2 = 44 = 1 feet. The ball goes 1 feet high.
💡 How to solve: Word Problems
For rows that grow by the same amount, use the arithmetic sequence formula aₙ = a₁ + (n - 1)d. For a function model like P(m), substitute the given number for m and simplify.
Try a similar one
A ball is dropped from 16 feet. Each bounce reaches half the height of the one before. How high does it go on bounce 3?
✓ 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 = 4 into the model: P(4) = 3 × 4 + 4 = 12 + 4 = 16. The profit is 16 dollars.
✓ Correct!
Not quite. The answer is
💡 Substitute m = 4 into the model: P(4) = 3 × 4 + 4 = 12 + 4 = 16. The profit is 16 dollars.
💡 How to solve: Word Problems
For rows that grow by the same amount, use the arithmetic sequence formula aₙ = a₁ + (n - 1)d. For a function model like P(m), substitute the given number for m and simplify.
Try a similar one
A ball is dropped from 40 feet. Each bounce reaches half the height of the one before. How high does it go on bounce 3?
✓ 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
💡 The rows grow by the same amount each time, so this is an arithmetic sequence: a_n = a_1 + (n − 1)d with a_1 = 15 and d = 4. a_5 = 15 + (5 − 1) × 4 = 15 + 16 = 31 seats. Row 5 has 31 seats.
✓ Correct!
Not quite. The answer is
💡 The rows grow by the same amount each time, so this is an arithmetic sequence: a_n = a_1 + (n − 1)d with a_1 = 15 and d = 4. a_5 = 15 + (5 − 1) × 4 = 15 + 16 = 31 seats. Row 5 has 31 seats.
💡 How to solve: Word Problems
For rows that grow by the same amount, use the arithmetic sequence formula aₙ = a₁ + (n - 1)d. For a function model like P(m), substitute the given number for m and simplify.
Try a similar one
Rae saves $25 the first week and $4 more each week than the week before. How much has she saved in total after 12 weeks?
✓ 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 F = -49: C = (59)(-49 − 32) = (59) × (-81) = 5 × (-9) = -45. That is -45 degrees Celsius.
✓ Correct!
Not quite. The answer is
💡 Substitute F = -49: C = (59)(-49 − 32) = (59) × (-81) = 5 × (-9) = -45. That is -45 degrees Celsius.
💡 How to solve: Word Problems
For rows that grow by the same amount, use the arithmetic sequence formula aₙ = a₁ + (n - 1)d. For a function model like P(m), substitute the given number for m and simplify.
Try a similar one
A job pays $20000 in the first year, with a raise of $2500 every year after. What is the pay in year 11?
✓ 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
💡 The pay goes up by the same raise each year, so this is an arithmetic sequence: a_n = a_1 + (n − 1)d with a_1 = $22,000 and d = $1,500. a_9 = 22,000 + (9 − 1) × 1,500 = 22,000 + 12,000 = 34,000. The pay in year 9 is $34,000.
✓ Correct!
Not quite. The answer is
💡 The pay goes up by the same raise each year, so this is an arithmetic sequence: a_n = a_1 + (n − 1)d with a_1 = $22,000 and d = $1,500. a_9 = 22,000 + (9 − 1) × 1,500 = 22,000 + 12,000 = 34,000. The pay in year 9 is $34,000.
💡 How to solve: Word Problems
For rows that grow by the same amount, use the arithmetic sequence formula aₙ = a₁ + (n - 1)d. For a function model like P(m), substitute the given number for m and simplify.
Try a similar one
A ball is dropped from 4 feet. Each bounce reaches half the height of the one before. How high does it go on bounce 2?
✓ 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
💡 Set T(t) = 60 and solve: 144 − 3t = 60. Subtract 60 from both sides and add 3t: 84 = 3t. Divide both sides by 3: t = 28. It is 60 degrees after 28 minutes.
✓ Correct!
Not quite. The answer is
💡 Set T(t) = 60 and solve: 144 − 3t = 60. Subtract 60 from both sides and add 3t: 84 = 3t. Divide both sides by 3: t = 28. It is 60 degrees after 28 minutes.
💡 How to solve: Word Problems
For rows that grow by the same amount, use the arithmetic sequence formula aₙ = a₁ + (n - 1)d. For a function model like P(m), substitute the given number for m and simplify.
Try a similar one
A ball is dropped from 16 feet. Each bounce reaches half the height of the one before. How high does it go on bounce 2?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
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Word Problems — Easy Worksheet 2
Read each problem and solve.