Here is the question:
"To make a pancake mix, add 1/2 cup of sugar, 3 cups of flour, 1 cup of powdered milk, 1 teaspoon baking powder and 1/2 teaspoon salt. Assuming the volume of the baking powder and salt are negligible, how much flour will be needed to make 50 cups of the dry mix?"
We are doing proportions, which is:
a= c
over
b d
***The units of A&C have to be the same and B&D also.
I got this far in the problem while doing it::::
x (cups of flour) = ???
________________ = _________
50 cups of flour 3 cups of flour
for the top ?? do I put all the dry ingredients listed in the question asked? Because I don't think I do, because if I did so, then the outcome would be too large, wouldn't it?
And then it asks:
"List the ingredients to a favorite recipe. Triple the recipe."
then
"Now figure 1/3 the recipe. Try using fraction multiplication, then do the problem again using proportion method."
The recipe I chose was this::
FRUIT SALAD
1 pint of strawberries
1 pound of grapes
3 bananas
1 (8 oz) strawberry yogurt.
I'm really stupid.
So to triple the recipe that I write, I would times it by 3, correct?
But when it tells me to do 1/3 of the recipe I keep getting the tripled amount.
Am I doing something wrong?
You have 3 cups flour + 1/2 cup sugar + 1 cup dry milk = 4.5 cups total dry mix.
Now the proportion is
(cups flour/old dry mix) =(new cups flour/new dry mix).
(3/4.5)=(?/50)
Cross multiply to obtain
3*50 = 4.5*?
? = (3*50/4.5) = ??cups flour in 50 cups of dry mix.
For the favorite recipe, the problem says to figure 1/3 the recipe; therefore, multiply by 1/3. You are multiplying by 3 if you are tripling it.
1 pt x 1/3 = 1/3 pt strawberries,
1 pound x 1/3 = 1/3 pound grapes,
3 bananas x 1/3 = 1 banana,
1 cup yogurt x 1/3 = 1/3 cup strawberry yogurt.
I went back and reread the problem. I think it is asking
1. First, to triple the recipe, which means you WOULD multiply by 3.
2. Then the problem asks you to figure 1/3 the recipe and I worked that part.
Let's break down the problem and solve it step by step.
Question 1: How much flour will be needed to make 50 cups of the dry mix?
We are given the following proportions:
1/2 cup of sugar = 3 cups of flour
1 cup of powdered milk = 3 cups of flour
1 teaspoon baking powder = 3 cups of flour
1/2 teaspoon salt = 3 cups of flour
To find out how much flour will be needed for 50 cups of the dry mix, we can use a proportion:
x (cups of flour) / 50 cups of flour = 3 cups of flour / 1 ingredient
To get the value of x (cups of flour), we cross multiply and solve for x:
x = (50 cups of flour * 3 cups of flour) / 1 ingredient
x = 150 cups of flour / 1 ingredient
x = 150 cups of flour
Therefore, you would need 150 cups of flour to make 50 cups of the dry mix.
Now let's move on to the next question.
Question 2: List the ingredients for a favorite recipe. Triple the recipe.
The original recipe you chose is:
- 1 pint of strawberries
- 1 pound of grapes
- 3 bananas
- 1 (8 oz) strawberry yogurt
To triple the recipe, you would multiply each ingredient by 3:
- 3 pints of strawberries
- 3 pounds of grapes
- 9 bananas
- 3 (8 oz) strawberry yogurts
Finally, let's tackle the last question.
Question 3: Figure out 1/3 of the recipe using fraction multiplication, then do the problem again using the proportion method.
To find 1/3 of the recipe using fraction multiplication, you would multiply each ingredient by 1/3:
- 1/3 pint of strawberries
- 1/3 pound of grapes
- 1 banana
- 1/3 (8 oz) strawberry yogurt
Now, let's solve the problem using the proportion method. Let's say x represents 1/3 of the recipe.
x (1/3 of the recipe) / 1 = 1/3 (1 ingredient) / original ingredient
To get the value of x, we cross multiply and solve for x:
x = 1/3 (1 ingredient) * 1 / original ingredient
x = 1/3 ingredient / original ingredient
So, 1/3 of the recipe would be 1/3 the amount of each ingredient in the original recipe.
I hope this helps clarify the steps to solve these questions! Let me know if you have any further questions.