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Sagot :
Let's break down the problem step-by-step and analyze each part to see if Marcos' equation accurately calculates the cost of milk needed for the recipe.
### Step 1: Determine the total cups of milk needed
Marcos needs [tex]\( 31 \frac{1}{4} \)[/tex] cups of milk. We can convert this mixed number to an improper fraction:
[tex]\[ 31 \frac{1}{4} = \frac{31 \times 4 + 1}{4} = \frac{124 + 1}{4} = \frac{125}{4} \][/tex]
So, Marcos needs [tex]\(\frac{125}{4}\)[/tex] cups of milk.
### Step 2: Convert cups of milk to gallons
We know that there are 4 cups in a gallon. Thus, the number of gallons of milk needed can be found by dividing the total cups of milk by 4:
[tex]\[ \frac{125}{4} \div 4 = \frac{125}{4} \times \frac{1}{4} = \frac{125}{16} \][/tex]
So, Marcos needs [tex]\(\frac{125}{16}\)[/tex] gallons of milk.
### Step 3: Calculate the cost of the milk
The cost of one gallon of milk is [tex]\( \$2.49 \)[/tex]. Therefore, the cost for [tex]\(\frac{125}{16}\)[/tex] gallons of milk is:
[tex]\[ \frac{125}{16} \times 2.49 \][/tex]
Let's break this multiplication into Marcos' equation form:
[tex]\[ \text{Cost} = \left(31 \frac{1}{4} \div 4\right) \times 2.49 \][/tex]
Rewriting our problem in the exact same form:
[tex]\[ \text{Cost} = \left(\frac{125}{4} \times \frac{1}{4}\right) \times 2.49 \][/tex]
[tex]\[ \text{Cost} = \left(\frac{125}{16}\right) \times 2.49 \][/tex]
### Step 4: Finding the total cost
When we carry out the final multiplication:
[tex]\[ \frac{125}{16} \times 2.49 \approx 19.453125 \][/tex]
Thus, the total cost to buy the milk is $19.453125.
### Conclusion
Marcos has correctly set up the equation to calculate the cost of milk by dividing the total number of cups needed by the number of cups in a gallon and then multiplying by the cost per gallon. The equation:
[tex]\[ \text{Cost} = \left(31 \frac{1}{4} \div 4\right) \times 2.49 \][/tex]
accurately describes the cost calculation. Therefore, Marcos' equation is accurate and correctly determines the total cost for the necessary amount of milk.
### Step 1: Determine the total cups of milk needed
Marcos needs [tex]\( 31 \frac{1}{4} \)[/tex] cups of milk. We can convert this mixed number to an improper fraction:
[tex]\[ 31 \frac{1}{4} = \frac{31 \times 4 + 1}{4} = \frac{124 + 1}{4} = \frac{125}{4} \][/tex]
So, Marcos needs [tex]\(\frac{125}{4}\)[/tex] cups of milk.
### Step 2: Convert cups of milk to gallons
We know that there are 4 cups in a gallon. Thus, the number of gallons of milk needed can be found by dividing the total cups of milk by 4:
[tex]\[ \frac{125}{4} \div 4 = \frac{125}{4} \times \frac{1}{4} = \frac{125}{16} \][/tex]
So, Marcos needs [tex]\(\frac{125}{16}\)[/tex] gallons of milk.
### Step 3: Calculate the cost of the milk
The cost of one gallon of milk is [tex]\( \$2.49 \)[/tex]. Therefore, the cost for [tex]\(\frac{125}{16}\)[/tex] gallons of milk is:
[tex]\[ \frac{125}{16} \times 2.49 \][/tex]
Let's break this multiplication into Marcos' equation form:
[tex]\[ \text{Cost} = \left(31 \frac{1}{4} \div 4\right) \times 2.49 \][/tex]
Rewriting our problem in the exact same form:
[tex]\[ \text{Cost} = \left(\frac{125}{4} \times \frac{1}{4}\right) \times 2.49 \][/tex]
[tex]\[ \text{Cost} = \left(\frac{125}{16}\right) \times 2.49 \][/tex]
### Step 4: Finding the total cost
When we carry out the final multiplication:
[tex]\[ \frac{125}{16} \times 2.49 \approx 19.453125 \][/tex]
Thus, the total cost to buy the milk is $19.453125.
### Conclusion
Marcos has correctly set up the equation to calculate the cost of milk by dividing the total number of cups needed by the number of cups in a gallon and then multiplying by the cost per gallon. The equation:
[tex]\[ \text{Cost} = \left(31 \frac{1}{4} \div 4\right) \times 2.49 \][/tex]
accurately describes the cost calculation. Therefore, Marcos' equation is accurate and correctly determines the total cost for the necessary amount of milk.
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