Applications of Simple Equations

• Translate word problems from daily life into simple linear equations.
• Define a variable for the unknown quantity (e.g. let x be the number of notebooks).
• Form an equation from given conditions and solve it.
• Interpret the solution in context — check that it is reasonable.

1. Problem-solving framework (CBSE / NCERT)

   1. Read the problem carefully; identify what is unknown.
   2. Let a letter (usually x, y, or n) represent the unknown.
   3. Express other quantities in terms of the variable.
   4. Write an equation using the given relationship.
   5. Solve the equation.
   6. State the answer with appropriate units and verify.

2. Common problem types in Class 7

   • Number problems: "A number increased by 8 equals 25."
   • Age problems: "Father is 3 times as old as son; sum of ages is 48."
   • Geometry: Perimeter and angle-sum problems.
   • Money and shopping: Cost of items, change, total bill.
   • Consecutive integers: "Three consecutive numbers sum to 42."

3. Translating phrases into algebra

   • "5 more than a number" → x + 5
   • "3 less than twice a number" → 2x − 3
   • "Sum of a number and 12 is 30" → x + 12 = 30
   • "Perimeter of a square is 36 cm" → 4s = 36

4. Checking reasonableness — A negative number of apples or a negative age usually means the equation was set up incorrectly. Re-read the problem.

5. Multiple conditions — Some problems give two facts; combine them into one equation or use one to express a second unknown.

Think of a number. Add 15 to it. The result is 42. Find the number.

Step 1 — let the number be x
Step 2 — condition: x + 15 = 42
Step 3 — solve: x = 42 − 15 = 27
Verify: 27 + 15 = 42 ✓
Answer: The number is 27.

The perimeter of a rectangular field is 120 m. Its length is 10 m more than its breadth. Find the length and breadth.

Step 1 — let breadth = b metres; then length = (b + 10) m
Step 2 — perimeter equation: 2 × (length + breadth) = 120
         2 × ((b + 10) + b) = 120
Step 3 — simplify: 2(2b + 10) = 120 → 4b + 20 = 120
Step 4 — 4b = 100 → b = 25
Step 5 — length = b + 10 = 35 m
Verify: 2(35 + 25) = 2(60) = 120 ✓
Answer: breadth = 25 m, length = 35 m

• "A number decreased by 9 equals 16." Write and solve the equation. (x − 9 = 16; x = 25)
• Sum of three consecutive integers is 54. Find them. (17, 18, 19)
• 3 notebooks and 2 pens cost ₹85; each notebook costs ₹15. Write an equation for the pen price p. (3×15 + 2p = 85)

Open the Practice tab for graded application problems on simple equations.