How to solve word problems — translate English to algebra step by step

Question

Ravi is 7 years older than his sister Priya. Five years from now, Ravi’s age will be twice Priya’s age. Find their present ages.

(CBSE 7-9 standard word problem)

The Translation Algorithm

flowchart TD
    A["Read the word problem"] --> B["Identify the unknowns"]
    B --> C["Assign variables"]
    C --> D["Translate each sentence to an equation"]
    D --> E["Solve the equation(s)"]
    E --> F["Check: does the answer make sense?"]
    F -->|No| G["Re-read and fix the setup"]
    F -->|Yes| H["Write the final answer"]
    D --> D1["'more than' = +"]
    D --> D2["'less than' = -"]
    D --> D3["'times' / 'twice' = multiply"]
    D --> D4["'is' / 'was' / 'will be' = equals sign"]

Solution — Step by Step

Let Priya’s present age = $x$ years.

Then Ravi’s present age = $x + 7$ years (he is 7 years older).

We used one variable because the second unknown is expressed in terms of the first.

“Five years from now, Ravi’s age will be twice Priya’s age.”

Priya’s age after 5 years = $x + 5$
Ravi’s age after 5 years = $(x + 7) + 5 = x + 12$

The equation: $x + 12 = 2(x + 5)$

x + 12 = 2x + 10

12 - 10 = 2x - x

x = 2

Priya’s age = $2$ years. Ravi’s age = $2 + 7 = 9$ years.

\boxed{\text{Priya} = 2 \text{ years},\quad \text{Ravi} = 9 \text{ years}}

Five years from now: Priya = 7, Ravi = 14. Is $14 = 2 \times 7$ ? Yes. The answer checks out.

Why This Works

Word problems are just equations hiding behind English sentences. The skill is translation — converting words into mathematical symbols. “Is” becomes $=$ , “more than” becomes $+$ , “twice” becomes $2 \times$ , “from now” means add years.

Once the equation is set up correctly, solving it is straightforward algebra. The hard part is always the translation, not the solving. That is why verification matters — plug the answer back into the original words, not just the equation.

Alternative Method — Using Two Variables

Let $r$ = Ravi’s age, $p$ = Priya’s age.

Equation 1: $r = p + 7$

Equation 2: $r + 5 = 2(p + 5)$

Substituting Equation 1 into Equation 2: $p + 7 + 5 = 2p + 10$ , giving $p = 2$ and $r = 9$ .

Age problems follow a pattern: set up the relationship now, then set up the relationship at the other time (past or future). You will always get one equation per condition. With two unknowns, you need two conditions — which is exactly what the problem gives.

Common Mistake

The biggest trap in age problems: when the problem says “5 years ago,” students subtract 5 from one person but forget the other. Both people age at the same rate. If Priya was $x - 5$ years old 5 years ago, Ravi was $(x + 7) - 5 = x + 2$ years old — not $x + 7$ .

Also, watch out for “years younger” vs “years older”. “Ravi is 7 years older than Priya” means $R = P + 7$ , not $P = R + 7$ .