Which quantity should you call x?
FNEGE’s description of the Calculation subtest emphasizes modeling word problems. This Upsilar workshop compares possible approaches; none is a universal shortcut. The two fictional Upsilar exercises show how to solve a problem and check the answer.
When possible, choose the quantity being asked for. Define it with its unit: “x is the number of adult tickets,” rather than writing x alone. Then translate the relationships one at a time. A difference often leads to addition or subtraction; a total combines contributions; “three times” signals multiplication.
Keep the constraints with the equation. A number of tickets must be a nonnegative integer. A duration cannot be negative. An algebraic solution that violates these conditions does not answer the problem. Multiple-choice options can help you search, but they do not replace translating the prompt.
How can you avoid using two unknowns when one is enough?
The total lets you express one quantity in terms of the other. This substitution reduces the problem to one equation while keeping both categories visible.
Une association vend 18 billets. Le billet adulte coûte 12 €, le billet enfant 7 €. La recette est de 176 €. Combien de billets adultes a-t-elle vendus ?
Choose an answer.
The solution, step by step
10 billets adultes.
The method in action
- If x is the number of adult tickets, then the number of children’s tickets is 18 − x. The revenue equation is 12x + 7(18 − x) = 176.
- This gives 12x + 126 − 7x = 176, so 5x = 50 and x = 10. That leaves 8 children’s tickets; 120 + 56 = 176.
- Another method: 18 children’s tickets would bring in €126. Each adult ticket adds €5. The additional €50 therefore corresponds to 50 ÷ 5 = 10 adult tickets.
When can the answer choices simplify the problem?
Testing choices is useful when each one can be checked quickly against every relationship. Do not choose a number just because it satisfies part of the prompt.
Lina a 6 ans de plus que Noé. Dans 4 ans, Lina aura le double de l’âge que Noé avait il y a 2 ans. Quel âge a Noé aujourd’hui ?
Choose an answer.
The solution, step by step
14 ans.
The method in action
- If x is Noé’s current age, Lina is x + 6. In 4 years, Lina will be x + 10; two years ago, Noé was x − 2.
- The equation is x + 10 = 2(x − 2). So x + 10 = 2x − 4, and x = 14.
- Testing 14: Lina is 20 and will be 24; Noé was 12, and 2 × 12 = 24. The choice satisfies both relationships and all the dates.
The pitfall
Changing the date attached to a quantity midway
In the second exercise, doubling Noé’s current age gives 2x; doubling his past age gives 2(x − 2). The challenge is not difficult calculation but translation. Match each age to the person and date before expanding.
Another common mistake: 2(x − 2) is not 2x − 2. The factor multiplies every term inside the parentheses. Expand only when it actually simplifies the solution; parentheses can also preserve the meaning of the statement.
How can you choose without trying every approach?
If the relationship immediately gives a simple equation, solve it. If a fixed total lets you compare with a reference case, such as all tickets being sold at the children’s price, that approach may be shorter. If the choices are easy to check, test one and verify every condition.
After reviewing, explain why your method fit the numbers in the problem. You do not need to solve every problem three ways during a timed session. Comparing methods is mainly for learning; when answering, choose one clear approach and then do an independent check.
Key takeaways
- Define the unknown with its unit and constraints.
- Translate dates and parentheses before calculating.
- An answer choice is valid only if it satisfies the entire prompt.