How to translate a word problem into an equation without keyword tricks

Suppose a co-working room charges a fixed booking fee of €24 plus €18 per hour. The final charge is €78. The question asks for the number of hours. Before calculating, name the unknown: let $h$ be the booked time in hours. Let $C$ represent the total charge in euros.

This small step separates quantities from the numbers that describe them. The symbols now have meanings and units: $h$ is measured in hours, while $C$ is measured in euros. An equation can be checked against both, which makes it harder to combine values simply because they appear in the same sentence.

The pricing rule is not hidden in a particular word. It is a relationship: total charge = fixed fee + hourly charge × hours. Translating that complete statement gives $C=24+18h.$ Since the problem says the total is €78, we can write $78=24+18h.$

Writing the verbal relationship first prevents a common mistake: reaching for an operation before deciding what it represents. The word “plus” happens to appear here, but the structure matters more. If the description said the booking fee was included in the total, the same addition would still be required even without that keyword.

The term $18h$ has units of euros because €18 per hour is multiplied by a number of hours. Adding the €24 fixed fee therefore produces another amount in euros, matching $C$. The equation is dimensionally coherent.

A tempting but incorrect expression such as $24h+18$ would say that the booking fee grows with every hour while the hourly charge is fixed. Its units and meaning contradict the description. Unit checks do not solve the whole problem, but they can reject an equation whose arithmetic still looks plausible.

Now the algebra has a purpose. From $78=24+18h,$ subtract $24$ from both sides to isolate the variable term: $54=18h.$ Dividing both sides by $18$ gives $h=3$.

Interpret the result in the original context: the room was booked for three hours. Then check it using the pricing rule: $24+18(3)=24+54=78.$ The numerical total, the units, and the meaning all agree. A bare answer of $3$ would omit the unit that tells us what the result represents.

Words such as more, per, of, and left can occur in different structures. “Five more than $x$” means $x+5$, while “$x$ is five more than $y$” means $x=y+5$. The word more does not determine which quantity stands on which side of the equation.

Likewise, per describes a rate, but whether to multiply or divide depends on what is known. At €18 per hour, hours produce a cost through multiplication; a known cost can produce hours through division. Instead of memorizing a word-to-operation table, ask which quantity changes, what it changes with, and which quantity is fixed.

For a new problem, write four short lines before solving: unknown and unit; known quantities and units; relationship in words; relationship in symbols. Then test whether each term has compatible units and whether increasing the unknown changes the result in the expected direction.

If the symbolic step remains unclear, ask for the smallest useful hint: identify the fixed quantity, the rate, or the total rather than requesting the finished equation. The guides in Euler Learn model explicit relationships and checks, and you can open the tutor with your own problem when you want help choosing the next representation.