Question

9 gregory buys a 5-oz packet of oregano. how much oregano will he have left after making the taco seasoning? (a) ounces (b) gregorys mom says that the secret to good taco seasoning is to double the chili powder. if gregory takes his mother’s advice, how much chili powder should he use? (c) he has a 12-ounce container he wants to use to store his taco seasoning. will it be big enough? (assume gregory follows his mother’s advice and doubles the chili powder.) explain how you know. (d) gregory wants to make the taco seasoning from part c last 10 weeks. how many ounces can his family use each week?

Explanation:

To solve these problems, we need the recipe for taco seasoning (amount of each ingredient, especially oregano and chili powder) which is missing. Please provide the taco seasoning recipe (amounts of oregano, chili powder, and other ingredients used) so that we can calculate the required values. For example, if the recipe uses \( x \) ounces of oregano and \( y \) ounces of chili powder, we can proceed as follows:

Part (a)

Step 1: Identify oregano used

Let the amount of oregano used in the recipe be \( x \) ounces.

Step 2: Calculate remaining oregano

Subtract the oregano used from the total oregano bought. Total oregano bought is 5 ounces. So remaining oregano \( = 5 - x \) ounces.

Part (b)

Step 1: Identify original chili powder

Let the original amount of chili powder used in the recipe be \( y \) ounces.

Step 2: Double the chili powder

Multiply the original amount by 2. So new chili powder \( = 2y \) ounces.

Part (c)

Step 1: Calculate total taco seasoning

First, find the amount of each ingredient in the new recipe (with doubled chili powder) and sum them up. Let other ingredients (except oregano and chili powder) be \( z \) ounces. Total taco seasoning \( = (5 - x) + 2y + z \) ounces (assuming oregano left is \( 5 - x \), chili powder is \( 2y \), and other ingredients are \( z \)).

Step 2: Compare with container size

Compare the total taco seasoning with 12 ounces. If \( (5 - x) + 2y + z \leq 12 \), then the container is big enough; otherwise, it is not.

Part (d)

Answer:

Step 1: Identify total taco seasoning

From part (c), total taco seasoning is \( T = (5 - x) + 2y + z \) ounces.

Step 2: Divide by number of weeks

Divide the total taco seasoning by 10 weeks. So ounces per week \( = \frac{T}{10} = \frac{(5 - x) + 2y + z}{10} \) ounces.

Once you provide the recipe details (amounts of oregano, chili powder, and other ingredients used), we can substitute the values and give the numerical answers.