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Airida [17]
3 years ago
15

On the popular cooking show Cookbook Crunch, the host picks a random recipe from a cookbook and the author has to feed the 63-me

mber 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.)
Mathematics
1 answer:
otez555 [7]3 years ago
4 0

Answer:

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

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

<u>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!</u>

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Check the picture below.

so let's find the lengths of those two sides in red, since are the length and width of the rectangle.

\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-6}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{-3}~,~\stackrel{y_2}{6})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d = \sqrt{[-3-(-6)]^2+[6-3]^2}\implies d=\sqrt{(-3+6)^2+(6-3)^2} \\\\\\ d=\sqrt{9+9}\implies \boxed{d=\sqrt{18}} \\\\[-0.35em] ~\dotfill

\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-6}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{-2}~,~\stackrel{y_2}{-1})~\hfill d=\sqrt{[-2-(-6)]^2+[-1-3]^2} \\\\\\ d=\sqrt{(-2+6)^2+(-1-3)^2}\implies d=\sqrt{16+16}\implies \boxed{d=\sqrt{32}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{area of the rectangle}}{(\sqrt{18})(\sqrt{32})}\implies \sqrt{18\cdot 32}\implies \sqrt{576}\implies 24

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