7.EE.4 — Equations & Inequalities in the Real World
Practice setting up and solving real-world equations of the form px + q = r and p(x + q) = r using integers, fractions, and decimals to find unknown quantities.
Download
Three different problem sets — same skill, same layout, fresh numbers.
Preview — Set A
Read each word problem carefully, write the equation, and solve for the unknown variable.
- 1.Maya is saving money to buy a book that costs $12.75. She already has $4.50 saved. She writes the equation x + 4.50 = 12.75, where x is the amount she still needs to save. How much more money does Maya need?
- 2.A bag of apples weighs 3.6 pounds. After eating some apples, the bag weighs 1.9 pounds. Using the equation x + 1.9 = 3.6, where x is the weight eaten, how many pounds of apples were eaten?
- 3.Carlos earns $8.50 per hour at his part-time job. He wants to find out how many hours he must work to earn $59.50. He sets up 8.5h = 59.50. How many hours must Carlos work?
- 4.A recipe calls for 2/3 cup of sugar. Leah has already measured 1/4 cup. She writes x + 1/4 = 2/3 to find how much more sugar she needs. How much more sugar does Leah need?
- 5.A plumber charges a flat fee of $35 plus $25 per hour. The total bill was $110. The equation 25h + 35 = 110 represents this situation, where h is the number of hours worked. How many hours did the plumber work?
- 6.Jordan bought several notebooks at $1.75 each and spent a total of $10.50. Using the equation 1.75n = 10.50, where n is the number of notebooks, how many notebooks did Jordan buy?
- 7.A temperature drops by 4.5 degrees and reaches –2.3°F. The equation t – 4.5 = –2.3 models this situation, where t is the starting temperature. What was the starting temperature?
- 8.Three friends split a restaurant bill equally, and each person paid $14.60. Using the equation 3x = 43.80 to find the total bill, what was the total restaurant bill?
- 9.A school fundraiser raised a total of $276. Each student collected the same amount, and 12 students participated. Using 12x = 276, where x is the amount each student raised, how much did each student raise?
- 10.A rectangular garden has a length that is 5.2 meters more than its width. The length is 9.8 meters. Using the equation w + 5.2 = 9.8, where w is the width, find the width of the garden.
- 11.Sophia ran 1/2 mile in the morning and some more miles in the afternoon. She ran 2 3/4 miles total. The equation 1/2 + x = 2 3/4 represents this. How far did Sophia run in the afternoon?
- 12.A store is selling packs of trading cards for $3.25 each. Damon spent $19.50 on trading cards. Using 3.25p = 19.50, where p is the number of packs, how many packs did Damon buy?
- 13.Mia is thinking of a number. When she multiplies it by 6 and adds 4, she gets 34. The equation 6x + 4 = 34 represents this. What is the number Mia is thinking of?
- 14.A group of students each donated $2.50 to a charity jar. The jar now contains $17.50. Using 2.50s = 17.50, where s is the number of students, how many students donated?
- 15.A picture frame has a perimeter of 54 inches. The width is 11 inches. Using the equation 2(l + 11) = 54, where l is the length, find the length of the frame.
- 16.Tyler has some money. After spending $6.75 on lunch and $3.50 on a snack, he has $5.25 left. The equation x – 6.75 – 3.50 = 5.25 models this. How much money did Tyler start with?
- 17.A worker packs 1/3 of a crate of oranges per hour. After several hours, she has packed 4 crates. Using (1/3)h = 4, where h is the number of hours, how many hours did she work?
- 18.Four times a number, decreased by 7, equals 13. The equation 4n – 7 = 13 models this situation. What is the number?
- 19.A school bus can carry 48 passengers. After some students get off at the first stop, 31 students remain. Using the equation 48 – x = 31, where x is the number of students who got off, how many students got off at the first stop?
- 20.Elena buys 5 equally priced notebooks and a pen that costs $1.20. She pays $8.70 in total. Using the equation 5n + 1.20 = 8.70, where n is the cost of one notebook, find the cost of each notebook.
- 21.A swimming pool holds 12,000 gallons of water. It is being drained at a rate of 450 gallons per hour. Using 12000 – 450t = 7500, where t is time in hours, find after how many hours the pool will have 7,500 gallons remaining.
- 22.A cell phone plan charges a flat monthly fee of $15 plus $0.10 per text message. Last month's bill was $23.40. Using 0.10m + 15 = 23.40, where m is the number of texts sent, how many text messages were sent?
What this worksheet covers
22 story problems fill this word problems page; problem 8 asks "Three friends split a restaurant bill equally, and each…", and the sheet stays at that level throughout. The problems are written as situations that have to be translated before they can be calculated and several problems use mixed numbers, which have to be handled without dropping the whole-number part. Further down, problem 15 asks "A picture frame has a perimeter of 54 inches. The width is…". The sheet sits inside Common Core 7.EE.4, in the grade 7 Expressions & Equations strand.
Skills practised
At grade 7, expressions and equations is about two-step equations, the distributive property, like terms with signed coefficients and one-step inequalities, and this sheet takes one slice of that. Specifically, the problems practise equations & Inequalities in the Real World. Working the page asks a student to read a situation and choose an operation before computing, work in fractional units and give the answer in lowest terms, and keep the decimal points aligned.
About the word problems format
Story problems are set one to a line with room to work underneath, problem 8, "Three friends split a restaurant bill equally, and each…" among them, and the key gives each of the 22 answers with its unit. Translating a sentence into an equation is the skill the drill sheets cannot practise, and the one that matters most.
Set A, Set B and Set C
Set A is the original MathSheetLab worksheet; Sets B and C keep its structure and redraw the numbers, with each answer recomputed rather than copied. Where Set A's problem 12 is "A store is selling packs of trading cards for $3.25 each.…", Set B's is "A picture frame has a perimeter of 46 inches. The width is…".
22 story problem(s) drawn from the 7.EE.4 context family (equation stories with decimal and fraction coefficients) — parameters inferred from the standard and grade
How to use this worksheet
Expect twenty minutes or so of real attention for 22 problems. At grade 7, expressions and equations rewards care over speed — a rushed word problems gets the arithmetic right and the signs or units wrong. Use the key as a check, not as a grade; none of the 22 problems needs a score attached to be useful.
One mistake to watch for
The same operation is not done to both sides: x + 5 = 12 becomes x = 12 + 5. Watch problem 15 of this word problems — "A picture frame has a perimeter of 54 inches. The width is…" — for this one.
The equation is being read as instructions rather than as a balance.
Draw a line down through the equals sign and write the inverse operation on both sides of it, every time.
Other grade 7 expressions and equations formats
The same skill in the other formats available at this grade.
- Drill — Grade 7 Expressions & Equations Drill, 30 problems
- Timed Drill — Grade 7 Expressions & Equations Timed Drill, 60 problems
- Missing Number — Grade 7 Expressions & Equations Missing Number, 24 problems
- Mixed Review — Grade 7 Expressions & Equations Mixed Review, 30 problems
A step either side
The same format one grade down and one grade up — the easier sheet is often the faster fix when this one is not landing.
- 6.EE.7 — Writing & Solving Equations: Real-World Practice — grade 6, 22 problems
- Grade 8 Word Problems: Writing and Solving Linear Equations — grade 8, 14 problems
Word Problems sheets in other grade 7 topics
Six PDFs, no sign-up: three versions of this grade 7 expressions and equations word problems and three answer keys, each 22 problems long.