A certain recipe requires 3/2 cups of sugar

A certain recipe requires 3/2 cups of sugar and makes 2 dozen cookies. (1 dozen = 12) Quantity A : The amount of sugar required for the same recipe to make 30 cookies Quantity B : 2 cups Quantity A is greater., Quantity B is greater., The two quantities are equal., The relationship cannot be determined from the information given.

3 Explanations

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Annie Wang

Can you also set up proportions to solve? I ended up setting [(3/2)/24]=x/30 and solving for x.

Jan 29, 2018 • Comment

David Recine, Magoosh Tutor

You can indeed take that approach to solve for x. If that worked well for you and you were able to do it comfortably and quickly, it was your best personal approach. With that said, I don't know if I'd recommend it; placing a fraction within the numerator tends to complicate things greatly. Some students may find that challenging in this problem, and it can make things far too difficult in other ore complicated math problems.

Jan 30, 2018 • Reply

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Cydney Seigerman, Magoosh Tutor

Hi Estivaliz :)

When writing equations and using variables, it's important to define what the variable represents. It's also a good idea to keep track of your units, as this will help us verify that we have the correct answer :)

In the solution you suggest, x would be equal to the number of cookies that could be made using 1 cup of sugar. So, when we solve for x we see that we can make 16 cookies using 1 cup of sugar. Then, yes, as you suggested we could divide 30 cookies by this ratio to see that we need less than 2 cups of sugar to make 30 cookies:

30 cookies / (16 cookies/cups of sugar) = 1.876 cups of sugar

And, as you said, this value is less than 2 cups, the value under Quantity B.

Good job! I hope this helps :)

Nov 29, 2015 • Comment

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Chris Lele, Magoosh Tutor

Sep 22, 2012 • Comment

Estivaliz Castro

can you say 3/2x=24 to find out what is the multiple and then divide 30 by 16 and find it is less than two?

Nov 23, 2015 • Reply

Emma Muhleman

Yes, I think what you are trying to say is this, which I think is easier to explain using numbers with decimals.
You could say: 1.5 cups of sugar makes 24 cookies, thus to convert this into the number of cookies produced per cup of sugar, we'd have
24 cookies / 1.5 cups = 16 cookies made per 1 cup of sugar
Then, if we want to make 30 cookies, we will need:
30 cookies / 16 cookies per cup of sugar = 1,875 cups of sugar
Thus, Quantity A is 1.875 which is < 2, and your answer is B

Jan 5, 2018 • Reply

David Recine, Magoosh Tutor

That also works, Emma. And you're right; thinking about decimals and approaching the problem your way can be easier... if you have the number sense for it. ;)

Jan 8, 2018 • Reply

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A certain recipe requires 3/2 cups of sugar

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Section 5: Math

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