Problem:
Huey's Hip Pizza sells two sizes of square pizzas: a small pizza that measures 10 inches on a side and costs $10, and a large pizza that measures 15 inches on a side and costs $20. If two friends go to Huey's with $30 apiece, how many more square inches of pizza can they buy if they pool their money than if they each purchase pizza alone?
My thoughts:
Step 1 --
$30:
$10x3=$30 _ 10*2 x 3=300 square inches
$10+$20=$30 _ 10*2 + 15*2=325 square inches
so put them together, options are: 1) 300+300=600 2) 300+325=625 3) 325+325=650
Step 2 --
$60:
$10 x 6=$60 _ 10*2 x 6=600
$40+$20=$60 _ 10*2 x4+15*2=625
$20+$40=$60 _ 10*2 x2+15*2 x2=625
$20 x 3=$60 _ 15*2 x3=675
Step 3 -- conclusion
possibility 1: 675-600=75
or possibility 2: 675-625=50
or possibility 3: 675-650=25
However! The answer is below:
25 square inches: First, figure the area of each pizza: the small is 100 square inches, and the largeis 225 square inches. If the two friends pool their money, they can buy three large pizzas, which have atotal area of 675 square inches. If they buy individually, though, then each friend will have to buy onelarge pizza and one small pizza, so they will only have a total of 2(100 + 225) = 650 square inches ofpizza.
Why is my thinking against the answer??
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- julial838
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- RonPurewal
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Re: Two people buy Pizzas
the question asks "how many more square inches of pizza can they buy?"
there's only one reasonable way to address this question, and that is to find whatever is the MOST they can buy in each of the two scenarios.
you've done the work correctly, so, just take the biggest numbers from each part (= 650 and 675). there you go.
there's only one reasonable way to address this question, and that is to find whatever is the MOST they can buy in each of the two scenarios.
you've done the work correctly, so, just take the biggest numbers from each part (= 650 and 675). there you go.
- RonPurewal
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Re: Two people buy Pizzas
more generally, always keep in mind that there are no "tricks" in the wording of problems on this exam. NO tricks, ever.
the questions will always mean whatever they would mean to random people on the street.
in terms of the "can" question, as asked here-- let's say you walk into a butcher shop and ask the butcher, "How many of those pork chops can I get for $20?"
...you know what will happen: the butcher will tell you the largest number of pork chops that your $20 will buy. (s)he will most certainly NOT give an exhaustive list of possibilities.
you just need to address these problems with the same everyday intuition.
this realization is SUPER important, because, if you are constantly scanning the words for "sneaky tricks" (which will never actually be there), you'll have substantially less brainpower available for actual problem-solving. not a good situation, that.
the questions will always mean whatever they would mean to random people on the street.
in terms of the "can" question, as asked here-- let's say you walk into a butcher shop and ask the butcher, "How many of those pork chops can I get for $20?"
...you know what will happen: the butcher will tell you the largest number of pork chops that your $20 will buy. (s)he will most certainly NOT give an exhaustive list of possibilities.
you just need to address these problems with the same everyday intuition.
this realization is SUPER important, because, if you are constantly scanning the words for "sneaky tricks" (which will never actually be there), you'll have substantially less brainpower available for actual problem-solving. not a good situation, that.
3 posts Page 1 of 1