What you will be able to do
- Work each problem without looking at the answer.
- Write the algebraic step that justifies each change.
- Check the result in the original relationship.
- Use the error notes to decide what to practise next.
How to use this worksheet
For each problem, define the variable with units, write a mathematical model, solve it and interpret the result in one complete sentence.
- Define quantities and units
- Translate constant rate and starting value
- Write equations or inequalities
- Reject answers that do not fit the context
For a clean student copy, print this page and cover the worked solutions or select the problem pages in your browser’s print preview.
Practice problems
Problem 1
A gym charges a $25 sign-up fee plus $18 per month. The total is $151. How many months?
Problem 2
A tank contains 90 L and drains 6 L per minute. When will 42 L remain?
Problem 3
Tickets cost $12 and the budget is no more than $85. What is the maximum whole number of tickets?
Problem 4
Plan A costs $20 + $5 per use. Plan B costs $44 + $2 per use. When are costs equal?
Problem 5
A quantity begins at 200 and grows 10% each period. Find it after 3 periods.
Answer key with worked solutions
Problem 1
A gym charges a $25 sign-up fee plus $18 per month. The total is $151. How many months?
- 1.Let m be months.
- 2.Write 25 + 18m = 151.
- 3.18m = 126, so m = 7.
Answer: 7 months
Check: 25 + 18(7) = 151.
Problem 2
A tank contains 90 L and drains 6 L per minute. When will 42 L remain?
- 1.Let t be minutes.
- 2.Write 90 − 6t = 42.
- 3.−6t = −48, so t = 8.
Answer: 8 minutes
Check: 90 − 48 = 42.
Problem 3
Tickets cost $12 and the budget is no more than $85. What is the maximum whole number of tickets?
- 1.Write 12t ≤ 85.
- 2.t ≤ 7.083…
- 3.Use a whole number that keeps the inequality true.
Answer: 7 tickets
Check: 7 cost $84; 8 cost $96.
Problem 4
Plan A costs $20 + $5 per use. Plan B costs $44 + $2 per use. When are costs equal?
- 1.Write 20 + 5u = 44 + 2u.
- 2.3u = 24, so u = 8.
Answer: 8 uses
Check: Both cost $60.
Problem 5
A quantity begins at 200 and grows 10% each period. Find it after 3 periods.
- 1.Growth factor is 1.10.
- 2.Write 200(1.10)³.
- 3.Compute 200(1.331).
Answer: 266.2
Check: 200 → 220 → 242 → 266.2.
Use mistakes to choose the next step
Review solving equationsUse the 8-week study plan
| If this happened | Likely issue | Next practice move |
|---|---|---|
| Variable has no meaning or unit | Model setup incomplete | Write “Let x represent…” first |
| Initial value and rate reversed | Linear form confusion | Identify the amount at zero and the per-unit change |
| Decimal answer used when count must be whole | Context not interpreted | Round only in a direction that satisfies the condition |
When independent practice is not enough
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Useful answers
Frequently asked questions
What is the first step in an algebra word problem?
Define the unknown quantity and its units, then identify the relationship among quantities.
How do I check a model?
Substitute the solution, include units and decide whether the result is possible in the original context.
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Sources, scope and accuracy
The worked examples and practice questions on this page are original Cambridge Veritas learning materials, not released STAAR items. Curriculum and testing details can change; use the linked Texas Education Agency pages for current official information. Cambridge Veritas is not affiliated with or endorsed by TEA.