Question

Sally’s seashore rentals has snorkels available for $2 and fins for $1 Josiah has $10 to spend on rentals for himself and his parents. Write a two-variable inequality to determine if the point (3,3) represents a viable solution in this case

Answer 1

To write a two-variable inequality for the problem, we need to represent the situation mathematically. Let's assign variables for the number of snorkels and the number of fins:

Let:
- \( x \) = number of snorkels rented
- \( y \) = number of fins rented

The costs for the snorkels and fins are:
- Each snorkel costs $2, thus the total cost for snorkels is \( 2x \).
- Each fin costs $1, thus the total cost for fins is \( y \).

Josiah has a total of $10 to spend, which leads to the following inequality:

\[
2x + y \leq 10
\]

Now, we need to check if the point \( (3, 3) \) represents a viable solution to this inequality. In this case, we will substitute \( x = 3 \) and \( y = 3 \) into the inequality:

\[
2(3) + 3 \leq 10
\]

Calculating the left side:

\[
6 + 3 \leq 10
\]

\[
9 \leq 10
\]

This statement is true. Therefore, the point \( (3, 3) \) satisfies the inequality \( 2x + y \leq 10 \) and represents a viable solution for the number of snorkels and fins that Josiah can rent.