On the popular cooking show Cookbook Crunch, the host picks a random recipe from a cookbook and the author has to feed the 63-member studio audience in one hour! The host selects this recipe for Carlita: Spicy Spinach and Apricots (Feeds 6) Ingredients: • 1/2 kilogram spinach • 1/4 kilogram apricots • 1/5 kilogram jalapeno pastry • 1/10 kilogram pine nuts • Salt, pepper, and hot sauce Bake at 350° in a medium loaf pan for 45 minutes. Carlita only finds a hundred small, 175-gram loaf pans. If cooking time is proportional to the amount of mixture and if the oven holds 9 of these pans at once, how much time will be left in the show when Carlita pulls the last batch out of the oven? (Assume the time to mix ingredients, remove a batch from the oven, and put in the next one is insignificant.)

When Carlita pulls the last batch out of the oven, it will be left in the show 7.5 minutes.

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

The host selects this recipe for Carlita:

Spicy Spinach and Apricots (Feeds 6)

Ingredients:

1/2 kilogram spinach = 500 grams

1/4 kilogram apricots = 250 grams

1/5 kilogram jalapeno pastry = 200 grams

1/10 kilogram pine nuts = 100 grams

Total ingredients for 6 = 500 + 250 + 200 + 100 = 1,050 grams

Carlita only finds a hundred small, 175-gram loaf pans.

2. If cooking time is proportional to the amount of mixture and if the oven holds 9 of these pans at once, how much time will be left in the show when Carlita pulls the last batch out of the oven? (Assume the time to mix ingredients, remove a batch from the oven, and put in the next one is insignificant.)

Original recipe = 1,050 grams of ingredients baked at 350° in a medium loaf pan for 45 minutes

1,050/175 = 6 (It means that the amount you’re baking in a small pan is 1/6 the amount in the original recipe). Let's recall that bake time is proportional to how much you’re baking, then you bake each small pan for 45 mins/6  = 7.5 minutes (divide by 6 since small pan is 1/6 the size of recipe)

Now, we can calculate the number of batches needed to feed the 63 members of the studio audience:

Batches = Number of members/Number of small pans at once in the oven

Batches = 63/9 = 7

Finally, we can calculate the time needed for the 7 batches:

Total time = Number of batches * proportional time a small pan needed to bake 175 grams of ingredients

Total time = 7 * 7.5 minutes = 52.5 minutes

If Carlita has to pull the last batch out of the oven in less than an hour, it will be left in the show (60 - 52.5 = 7.5 minutes) . She even could feed nine more members of the audience!

care to share were the trapezoid shown is ?