Chef alonso is creating a recipe called spicy italian chicken with the following ingredients: 3/4 pound chicken,2 1/2 cups tomato sauce, 1 teaspoon oregano and 1/2 teaspoon of his special sauce. a) chef alonso wants each serving of the dish to include 1/2 pound of chicken. how many 1/2 pound servings does this recipe make? b) what is the number chef alonso should multiply the amount of chicken by so that the recipe will make 2 full servings, each with 1/2 pound of chicken? c) use the multiplier you found in part b to find the amount of all the ingredients in the new recipe d) chef alonso only has three measuring spoons: 1 teaspoon ,1/2 teaspoon , and 1/4 teaspoon .can he measure the new amounts of oregano and hot sauce exactly? explain why or why not

Answers:

A) This recipe makes 3/2=1.5 1/2 pound servings.

B) The Chef Alonso should multiply the amount of chicken by 4/3 so that the recipe will make 2 full servings, each with 1/2 pound of chicken.

C) Amount of all the ingredients in the new recipe:

1 pound chicken.

3 1/3 cups tomato sauce.

1 1/3 teaspoon oregano.

2/3 teaspoon Chef Alonso's special sauce.

D) No, he can not measure the new amounts of oregano and hot sauce exactly.

Solution:

A) Using a rule of three:

1 serving of the dish     includes     1/2 pound chicken

                x                    include      3/4 pound chicken (Recipe)

x=(1 serving of the dish)(3/4 pound chicken) / (1/2 pound chicken)

x=(3/4) / (1/2)

x=(3/4) (2/1)

x=(3*2)/(4*1)

x=6/4

x=(6/2) / (4/2)

x=3/2=1.5

B) We want 2 full servings each with 1/2 pound of chicken, then we need a total of 2*(1/2) pound of chicken=1 pound of chicken

The recipe is with 3/4 pound of chicken, then to obtain 1 pound we must multiply by x:

(3/4)x=1

Solving for x: Multiplying both sides of the equation by 4/3:

(4/3)(3/4)x=(4/3)(1)

x=4/3

C) Amount of all the ingredients in the new recipe:

1. Chicken: (3/4 pound)(4/3)=1 pound

2. Tomato sauce: (2 1/2 cups)(4/3)=[(2*2+1)/2](4/3)=[(4+1)/2](4/3)=(5/2)(4/3)=(5*4)/(2*3)=20/6=(20/2)/(6/2)=10/3=(9+1)/3=9/3+1/3=3 1/3 cups

3. Oregano: (1 teaspoon)(4/3)=4/3=(3+1)/3=3/3+1/3=1 1/3 teaspoon

4. Chef Alonso's special sauce: (1/2 teaspoon)(4/3)=(1*4)/(2*3)=4/6=(4/2)/(6/2)=2/3 teaspoon

D) Chef Alonso only has three measuring spoons: 1 teaspoon, 1/2 teaspoon,  and 1/4 teaspoon. Can he measure the new amounts of oregano and hot sauce exactly? Explain why or why not

No, because he needs to measure 1 1/3 teaspoon of oregano and he can not measure 1/3 teaspoon (he only has 1/2 teaspoon and 1/4 teaspoon).

He needs to measure 2/3 teaspoon of his special sauce and he can not measure this quantity, because he only has 1/2 teaspoon and 1/4 teaspoon.