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.
