Question

traiteur #3 :

• ce traiteur demande un montant de base fixe et un coût par personne selon le tableau suivant :

nombre de personnes	3	9	17
coût total en $	234	402	626

Explanation:

Let the fixed cost be \( F \) and the cost per person be \( p \). The total cost \( C \) for \( n \) people is given by the linear equation \( C = F + pn \).

Step 1: Set up equations from the table

For \( n = 3 \) and \( C = 234 \): \( 234 = F + 3p \)
For \( n = 9 \) and \( C = 402 \): \( 402 = F + 9p \)

Step 2: Subtract the first equation from the second

\( (F + 9p) - (F + 3p) = 402 - 234 \)
\( 6p = 168 \)
\( p = \frac{168}{6} = 28 \)

Step 3: Find the fixed cost \( F \)

Substitute \( p = 28 \) into \( 234 = F + 3p \):
\( 234 = F + 3(28) \)
\( 234 = F + 84 \)
\( F = 234 - 84 = 150 \)

We can verify with \( n = 17 \): \( C = 150 + 28(17) = 150 + 476 = 626 \), which matches the table.

Answer:

The fixed cost is \$150 and the cost per person is \$28. (If you needed a specific value, e.g., fixed cost: \$150, cost per person: \$28)