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The problem describes a situation where the price of gasoline in La Serena is modeled by the linear function:

\[
f(x) = 8x + 1047
\]

where $x$ is the number of weeks, and $f(x)$ represents the price of gasoline in pesos.

Let's solve the two parts of the problem:

### Part (a)
We are asked to find the week when the gasoline price will be approximately $1191.

To do this, set $f(x) = 1191$ and solve for $x$:

\[
1191 = 8x + 1047
\]

Subtract 1047 from both sides:

\[
1191 - 1047 = 8x
\]

\[
144 = 8x
\]

Now, divide both sides by 8:

\[
x = \frac{144}{8} = 18
\]

So, in week **18**, the gasoline price will be approximately $1191.

### Part (b)
We are asked to find the gasoline price in week 48.

Using the function $f(x)$, substitute $x = 48$:

\[
f(48) = 8(48) + 1047
\]

\[
f(48) = 384 + 1047 = 1431
\]

Therefore, the gasoline price in week 48 will be **1431 pesos**.

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Do you have any questions or need further details on these solutions?

Here are 5 related questions to expand on this:
1. How do we interpret the slope (8) of the function in terms of gasoline prices?
2. What would happen to the gasoline price if the function's

Si el precio de la gasolina en cierta semana en La Serena se modela a través de la función f(x) = 8x + 1047.
 a) ¿En qué semana el valor de la gasolina alcanzará un valor aproximado de $1191?
 b) Si las alzas continúan en forma sostenida, ¿Qué valor podría alcanzar la gasolina en la semana 48?

Solve a linear function representing the gasoline price in La Serena, modeled by f(x) = 8x + 1047. Learn when the gasoline price will reach $1191 and predict its price in week 48. This problem is suitable for Grades 8-10 and covers key concepts like solving linear equations.

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