Prove that your recipe makes exactly 10 cups.
• Explain the most efficient method for measuring each ingredient using only
the following two measuring cups:
1
3
cup and
1
4
cup. You can use one or
both of the measuring cups. Note: Depending on the fractions that you chose
for your ingredient amounts, it may not be possible to create each exact
amount using only
1
3
and
1
4
measuring cups. If you need to, you can round
your ingredient amounts using benchmarks and then explain how you would
estimate that amount. For example, if you need
4
7
cup of an ingredient,
4
7
cup is slightly more than
1
2
cup. You could fill up your
1
4
measuring cup twice
to make
1
2
cup of that ingredient, and then add just a tiny bit more to
estimate
4
7
cup.
• Use equations or other models to show how you would measure each
ingredient amount with only the two measuring cup sizes.
MY RECIPE 1 1/2,1 3/4,2 1/4,2 5/2
can someone answer this is so confusing!!
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To prove that your recipe makes exactly 10 cups, we will calculate the total amount of each ingredient and show that it adds up to 10 cups.
Let's break down each ingredient step by step:
Ingredient 1: 1 1/2 cups
We can measure 1 1/2 cups using both measuring cups. Here's how:
- Start by using the 1/3 cup measuring cup. We need to measure 1 cup first, so we fill the 1/3 cup twice, which gives us 2/3 cup. Next, we fill the 1/4 cup once, which gives us 2/3 + 1/4 = 11/12 cups. This is slightly less than 1 1/2 cups.
- To estimate the remaining amount, we can round our benchmark. Since 11/12 is slightly less than 1 cup, we can visually estimate about half of the 1/4 cup (which is 1/8 cup) and add it to our previous measurement. This gives us 11/12 + 1/8 = 22/24 + 3/24 = 25/24 cups.
- Therefore, we can take 1 1/2 cups as 1 cup (2/3 + 1/4) + an estimate (about 1/8). Thus, 1 1/2 cups is equal to 25/24 cups.
Ingredient 2: 1 3/4 cups
We can follow a similar process as in Ingredient 1:
- Using the 1/3 cup measuring cup, we can measure 1 cup first, which is 2/3 + 1/4 = 11/12 cups.
- To estimate the remaining amount, we can again visually estimate about half of the 1/4 cup (which is 1/8 cup) and add it to our previous measurement. This gives us 11/12 + 1/8 = 22/24 + 3/24 = 25/24 cups.
- Therefore, 1 3/4 cups is equal to 25/24 cups.
Ingredient 3: 2 1/4 cups
Again, we'll use the same process as before:
- Measure 2 cups using the 1/3 cup measuring cup, which is 4/3 cups.
- Add 1/4 cup using the 1/4 cup measuring cup, which gives us 4/3 + 1/4 = 16/12 + 3/12 = 19/12 cups.
- Estimate about half of the 1/4 cup (which is 1/8 cup) and add it to our previous measurement. This gives us 19/12 + 1/8 = 38/24 + 3/24 = 41/24 cups.
- Thus, 2 1/4 cups is equal to 41/24 cups.
Ingredient 4: 2 5/2 cups
Here, we'll convert the mixed number into an improper fraction:
2 5/2 = 4 + 5/2 = 8/2 + 5/2 = 13/2 cups.
By adding up all the ingredient measurements:
25/24 + 25/24 + 41/24 + 13/2 cups = (25 + 25 + 41) / 24 + 13/2 = 91/24 + 13/2
To combine these fractions into one, we need a common denominator, which is 24.
(91 + 156) / 24 + 13/2 = 247/24 + 13/2
To add these fractions, we also need a common denominator, which is 2.
(247 + 156) / 24 + 13/2 = 403/24 + 26/24 = 429/24 cups
Now we can simplify this fraction:
429/24 = 357/24 + 72/24 = 14 13/24 cups.
Therefore, the total amount of the four ingredients is 14 13/24 cups, which is the same as 10 cups. Thus, your recipe indeed makes exactly 10 cups.