Question 1125629: Kaylee is in first grade and her class is cresting pasta necklaces! There are two types of pasta to use on the necklace: long macaroni pieces and small rótele pieces. The directions are to have no more than 30 pieces of pasta on a necklace and each string is long enough to hold 15 macaroni noodles or 60 pieces of rótele.
Select all of the true statements below
A:kaylees necklace Can hold 9 macaroni noodles and 21 pieces of rótele.
B: kaylees necklace Can hold 13 macaroni noodles and 18 rótele
C: kaylees necklace Can have 30 pieces of rótele
D: kaylees necklace Can hold 16 macaroni noodles and 14 pieces of rótele
E: kaylees necklace Can have 5 macaroni noodles and 10 pieces of rótele
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! a string can hold either 15 macaroni pieces or 60 rotele pieces.
60 / 15 = 4.
that means the string can hold 4 times as many rotele pieces as macaroni pieces.
therefore 1 macaroni piece is equivalent to 4 rotele pieces in terms of the space that it takes on the necklace.
using this information, you can answer the question.
you can either convert all the pieces to equivalent macaroni pieces or to equivalent rotele pieces.
to avoid fractions, i would convert everything to equivalent rotele pieces.
you simply replace each macaroni piece with 4 rotele pieces and then count the number of equivalent and actual rotele pieces.
your questions are:
A: kaylees necklace Can hold 9 macaroni noodles and 21 pieces of rótele.
9 * 4 = 36 + 31 = 57 which is less than 60, so this statement is true.
B: kaylees necklace Can hold 13 macaroni noodles and 18 rótele.
13 * 4 = 52 + 18 = 70 which is greater than 60, so this statement is false.
C: kaylees necklace Can have 30 pieces of rótele
30 is less than 60 so this statement is true.
D: kaylees necklace Can hold 16 macaroni noodles and 14 pieces of rótele
16 * 4 = 64 + 14 = 78 which is greater than 60, so this statement is false.
E: kaylees necklace Can have 5 macaroni noodles and 10 pieces of rótele.
5 * 4 = 20 + 10 = 30 which is less than 60, so this statement is true.
it looks like the true statements are A, C, E.
but wait .........
the directions also state that the necklace can have no more than 30 pieces of pasta.
you had two things going here.
you had to make sure all the pieces would fit on the string and you had to make sure that you didn't have more than 30 pieces on the string, even if they could all fit.
to make sure that they fit on the string, converting to equivalent rotele pieces was appropriate.
to make sure that there were no more than 30 pieces on the string, you had to count each piece as one, regardless of how much space they took up on the string.
statement A is still true, because 9 + 21 = 30 pieces and 9 * 4 + 21 = 36 + 21 = 57 equivalent rotele pieces which the string could hold.
statement B is still false because 13 + 18 = 31 which is more than the number of pieces allowed and also because 13 * 4 = 52 + 18 = 70 equivalent rotele pieces which the string couldn't hold.
statement C is still true because the total number of pieces (30) was less than or equal to 30 and they could all fit on the string because the string could hold 60 rotele pieces.
statement D is still false because, even if there were less than or equal to 30 pieces (16 + 14 = 30), 16 * 4 + 14 = 78 equivalent rotele pieces which the string couldn't hold.
statement E is still true because there were less than or equal to 30 pieces total (15) and the number of equivalent rotele pieces was less than 60 (30).
so, A, C, and E is still your answer as best i can determine.
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