Justin wants to visit Caroline at the zoo and is trying to plan his day. The entrance ticket to the zoo costs $35, but he can also add on educational workshops. Each educational workshop costs an additional $19. Justin has a budget of $100 for his zoo day.

Question

Which linear equation represents the scenario in #3?

y=19x+35

y=35x

y=100x+19

y=45x−100

Answer 1

To represent Justin's budget and the costs associated with his trip to the zoo using a linear equation, we can break down the costs:

• The entrance ticket to the zoo costs $35.
• Each educational workshop costs an additional $19.
• Justin has a total budget of $100.

Let:

• \( y \) be the total cost of the zoo trip,
• \( x \) be the number of educational workshops Justin decides to participate in.

The total cost can be expressed as:

\[ y = 35 + 19x \]

This equation shows that the total cost \( y \) is the base ticket price ($35) plus the cost of the workshops ($19 per workshop).

Now, if we want to represent this in a linear equation format, we can rearrange it to highlight the maximum budget constraint:

\[ y = 19x + 35 \]

This means that for \( x \) workshops, the total cost increases linearly based on the number of workshops added to the basic ticket price.

Thus, the correct linear equation that represents the scenario is:

y = 19x + 35.