A rectangle has perimeter 36 cm. Its length is 8 cm and its width is x cm. Write an equation in the form 2(x + q) = r and solve for x.
Equation: ____________________
Solution: ____________________
CCSS 7.EE.B.4a · model, solve & compare approaches
Grade 7 Equation Word Problem Worksheets
Translate a situation into px + q = r or p(x + q) = r, solve it algebraically, then compare that sequence with the arithmetic operations you would perform if the unknown were not written as a variable.
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Equation Word Problems
Equation word problems · Grade 7 standard · Seed 271801
1.
2.
A rental costs $8 per hour plus a one-time $15 fee. The total is $47. Write an equation and find the number of hours h.
Equation: ____________________
Solution: ____________________
3.
Each ticket pack has 7 tickets. After combining x new packs with 2 packs already on hand, there are 98 tickets. Write an equation and solve for x.
Equation: ____________________
Solution: ____________________
4.
A club charges a $29 setup fee plus $8 per month. A member has paid $117 total. Write an equation and determine the number of months m.
Equation: ____________________
Solution: ____________________
5.
Each ticket pack has 3 tickets. After combining x new packs with 7 packs already on hand, there are 45 tickets. Write an equation and solve for x.
Equation: ____________________
Solution: ____________________
6.
Each ticket pack has 6 tickets. After combining x new packs with 7 packs already on hand, there are 90 tickets. Write an equation and solve for x.
Equation: ____________________
Solution: ____________________
7.
A rectangle has perimeter 32 cm. Its length is 8 cm and its width is x cm. Write an equation in the form 2(x + q) = r and solve for x.
Equation: ____________________
Solution: ____________________
8.
A club charges a $16 setup fee plus $13 per month. A member has paid $159 total. Write an equation and determine the number of months m.
Equation: ____________________
Solution: ____________________
9.
Each ticket pack has 8 tickets. After combining x new packs with 4 packs already on hand, there are 72 tickets. Write an equation and solve for x.
Equation: ____________________
Solution: ____________________
10.
A rectangle has perimeter 22 cm. Its length is 6 cm and its width is x cm. Write an equation in the form 2(x + q) = r and solve for x.
Equation: ____________________
Solution: ____________________
Construction rule: equations are built around known exact solutions, expression rewrites use exact rational arithmetic, 7.EE.3 money stays in integer cents, and inequality answer graphs are withheld until answers are revealed.
Turning a word problem into an equation
Define the unknown with a letter, find the fixed amount and the amount that repeats, and write an equation in the form of a fixed part plus a repeating part equals the total. Then solve it as a two-step equation and say what the answer means with its units. Check that the answer makes sense in the story.
Worked examples
- A taxi costs $3 plus $2 per mile, and the fare is $17. Write 3 + 2m = 17, so 2m = 14 and m = 7 miles.
- Maya has $40 and saves $15 each week. She wants $130, so 40 + 15w = 130, giving 15w = 90 and w = 6 weeks.
- A number divided by 4, plus 6, is 14. Write x/4 + 6 = 14, so x/4 = 8 and x = 32.
Common slips
- Writing the equation with the wrong structure, such as 3m + 2 = 17 for the taxi, which swaps the fixed fee and the per-mile cost.
- Not saying what the letter stands for, which makes it hard to check the answer.
- Leaving off the units. The answer to the taxi problem is 7 miles, not just 7.
How to use this worksheet
Ask students to start each problem with 'Let x be…' and to finish with a sentence that includes the units. The answer key gives the value of the unknown.
Common Core connection
- 7.EE.B.4 · Use variables and equations or inequalities to solve problems and explain solutions.
A practical match for the skill this worksheet practises, not a claim that one worksheet teaches or assesses the whole standard. Check the official math standards.
Note 1
Define what the variable represents before writing the equation.
Note 2
Match the order of quantities in the story to the structure of the equation instead of hunting for keywords alone.
Note 3
Example: 'a gym charges $25 plus $4 per class and the bill was $61' models as 4x + 25 = 61, so 4x = 36 and x = 9 classes.
Note 4
A per-unit rate is the p in px + q = r; a one-time fixed amount is the q. Sorting the two before writing the equation prevents keyword traps.
Note 5
The arithmetic solution and algebraic solution should use the same inverse-operation sequence even though one is written without a variable.
Continue the 7.EE progression
Move to another Grade 7 algebra skill
Quick answers
Do answer keys show the equation?
Yes. The key includes the modeled equation, the solution, and a short arithmetic-path comparison.
Are these only money problems?
No. Contexts rotate among rental fees, rectangle perimeter, ticket packs, and subscription-style totals.