anonymous
  • anonymous
I'm not sure how to do conversions. May someone help me please? Earl needs to fill juice cups for his little brother's birthday party. There are 25 juice cups and each juice cup holds 12 fluid ounces. The juice comes in 1-gallon bottles. How many 1-gallon bottles of juice will Earl need to purchase? (1 quart = 32 fluid ounces, 1 gallon = 4 quarts)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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mathstudent55
  • mathstudent55
You can start with the number of cups and how much they hold. There are 25 cups. Each cup holds 12 fl oz. How many fluid ounces total are needed?
anonymous
  • anonymous
300 fl oz.
anonymous
  • anonymous
25*12= 300

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mathstudent55
  • mathstudent55
Great. We have 300 fl oz. Now we need to covert that to gallons.
mathstudent55
  • mathstudent55
Since we have conversion factors from fl oz to qt and from qt to gal, let's do the conversion in two steps.
mathstudent55
  • mathstudent55
Each conversion factor you apply is multiplied or divided by the number you have. Remember this, conversion factors are multiplied or divided.
anonymous
  • anonymous
So would you divide 300 by 32? which is 1qt.
anonymous
  • anonymous
Which would equal 9.
mathstudent55
  • mathstudent55
The conversion factor from fl oz to qt is 32. Now we need to decide if we multiply or divide.
mathstudent55
  • mathstudent55
This is how you decide. If 1 qt is 32 fl oz, what unit is larger, a qt or a fl oz?
anonymous
  • anonymous
A qt
mathstudent55
  • mathstudent55
Right. Since a qt is larger than a fl oz, if you have a certain volume, like we have 300 fl oz, it will be fewer number of qts than the number of fl oz. The same volume in qt and in fl oz will be a larger number in fl oz than in qt since a qt is larger than a fl oz. Do you understand this?
anonymous
  • anonymous
Yes I understand.
mathstudent55
  • mathstudent55
Here is an example to make this clearer. 1 foot equals 12 inches. 1 foot and 12 inches are exactly the same length. When you use the larger unit, ft, you have only 1, a smaller number. When you use the smaller unit, inches, you have 12, a larger number. In general, the same quantity, length, volume, area, etc. if measured with small units will give you larger number, if measured with larger units will give you a smaller number.
mathstudent55
  • mathstudent55
Great. Back to our problem.
mathstudent55
  • mathstudent55
The conversion factor between fl oz and qt is 32. We now need to decide if we multiply 300 fl oz by 32 or divide by 32 to get qt. 300 fl oz is measured in a small unit, fl oz. We now want it in qt, a larger unit. Since the number of qt must be less than 300, we must divide 300 by 32 to get qt.
anonymous
  • anonymous
300/32= 9.3qts
mathstudent55
  • mathstudent55
Good, but for now, keep it as 9.375 qt. Round it off in the last step after converting to gallons. After you divide 300 fl by 32, you have the volume in qt. Now you need to go from qt to gal. Again, you are going from a smaller unit, qt, to a larger unit, gal. That means there will be fewer gallons than quarts, so you need to divide by the conversion factor to get a smaller number. The conversion factor from qt to gal is 4, so divide the number of qt by 4 to get gal.
anonymous
  • anonymous
So 9.375/4 = 2.343
mathstudent55
  • mathstudent55
Correct. That is the volume in gallons. What is the final answer? How many gallons of juice must Earl buy?
anonymous
  • anonymous
3 gallons
mathstudent55
  • mathstudent55
That is correct. In this type of problem, the final answer must be rounded up. You got it. Great job!
anonymous
  • anonymous
Thank you very much I appreciate your help!
mathstudent55
  • mathstudent55
You're welcome.

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