Question

a recipe for 12 waffles calls for 1 1/2 cups of milk 2 1/4 cups of flour in 1 1/3 cups of other ingredients.A. what is the total number of cups of ingredients needed for 12 waffles? B. what is the total number of cups of ingredients needed for a 36 waffles? C. if the milk is reduced to 1 cup in the amount of other ingredients ( not including the flour) is increased to 2 cups, would the total amount of ingredients for 12 waffles increase or decrease from the original recipe? justify your thinking. D. if a baker has a 5lb bag of flour, which is approximately 17 cups of flour, how many complete recipes for a 12 waffles can the baker make? justify your thinking

Answer 1

A. 61/12 cups.

B. 61/4 cups

C. Since the increase in other ingredients is greater then the decrease, the total amount of ingredients increase.

D. 7 full recipes

Explanation:

A. what is the total number of cups of ingredients needed for 12 waffles?

We add the cups for each ingredient. So

`1(1)/(2)+2(1)/(4)+1(1)/(3)=(2\ast1+1)/(2)+(2\ast4+1)/(4)+(3\ast1+1)/(3)`
`(2\ast1+1)/(2)+(2\ast4+1)/(4)+(3\ast1+1)/(3)=(3)/(2)+(9)/(4)+(4)/(3)=\frac{3\ast6+9\ast3+4\ast4_{}}{12}`
`\frac{3\ast6+9\ast3+4\ast4_{}}{12}=(18+27+16)/(12)=(61)/(12)`

61/12 cups.

B. what is the total number of cups of ingredients needed for a 36 waffles?

36/12 = 3. So

3*(61/12) = 61/4

C. if the milk is reduced to 1 cup in the amount of other ingredients ( not including the flour) is increased to 2 cups, would the total amount of ingredients for 12 waffles increase or decrease from the original recipe?

Milk is reduced by 1/2(1/2 - 1);

Other ingredients are increased by 2/3(2 - 1 and 1/3).

Since the increase in other ingredients is greater then the decrease, the total amount of ingredients increase.

D. if a baker has a 5lb bag of flour, which is approximately 17 cups of flour, how many complete recipes for a 12 waffles can the baker make? justify your thinking

For one recipe: 9/4 cups

For 17 cups, x recipes

1 recipe - 9/4 cups

x recipes - 17 cups

`(9)/(4)x=17`
`x=(17\ast4)/(9)=(68)/(9)=7\ldots`

7 full recipes