The given problem describes a situation where an owner sells ski goggles and waterproof gloves for $24 each, and the function $f(x) = 24(x + 16)$ represents the total earnings from selling $x$ pairs of ski goggles and 16 pairs of waterproof gloves.

The question asks about the meaning of $f(32) = 1,152$.

Let's break this down:

• The function formula is $f(x) = 24(x + 16)$, which suggests that for each pair of ski goggles sold (represented by $x$), the total earnings is $24 times the sum of $x$ pairs of ski goggles and 16 pairs of waterproof gloves.
• To find $f(32)$, substitute $x = 32$ into the formula:

$f(32) = 24(32 + 16) = 24 \times 48 = 1,152$

This represents the total amount the owner earns when they sell 32 pairs of ski goggles and 16 pairs of waterproof gloves, which equals $1,152.

Thus, the correct interpretation is: The owner earns $1,152 by selling 32 pairs of ski goggles and 16 pairs of waterproof gloves.

So the correct option is: The owner earns $1,152 by selling 32 pairs of ski goggles and 16 pairs of waterproof gloves.

Would you like further details or explanations on this? Here are some follow-up questions to dive deeper:

1. How would the total earnings change if the owner sold 50 pairs of ski goggles and 16 pairs of waterproof gloves?
2. Can we modify the formula to account for different prices for the ski goggles and gloves?
3. How would you graph this function?
4. What would happen if the price of each item was doubled?
5. How would we calculate the earnings if the owner sold only waterproof gloves?

Tip: When interpreting functions in word problems, make sure to break down the components and substitute the known values carefully to interpret the meaning correctly!