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.
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.
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.
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
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. ;)
3 Explanations