Joseph is making kebabs. He wants each kebab to have
\[3\] pieces of meat and
\[4\] pieces of vegetables.
Which of the following could Joseph use to make kebabs without any leftovers?
Choose 3 answers:
Choose 3 answers:
(Choice A)
\[18\] pieces of meat and
\[30\] pieces of vegetables
A
\[18\] pieces of meat and
\[30\] pieces of vegetables
(Choice B)
\[20\] pieces of meat and
\[32\] pieces of vegetables
B
\[20\] pieces of meat and
\[32\] pieces of vegetables
(Choice C)
\[30\] pieces of meat and
\[40\] pieces of vegetables
C
\[30\] pieces of meat and
\[40\] pieces of vegetables
(Choice D)
\[45\] pieces of meat and
\[60\] pieces of vegetables
D
\[45\] pieces of meat and
\[60\] pieces of vegetables
(Choice E)
\[72\] pieces of meat and
\[96\] pieces of vegetables
E
\[72\] pieces of meat and
\[96\] pieces of vegetables
To make kebabs without any leftovers, Joseph needs to have a multiple of both 3 and 4 for the number of meat and vegetable pieces, respectively.
Choice A: 18 pieces of meat and 30 pieces of vegetables.
18 is a multiple of 3, but 30 is not a multiple of 4. Not a valid option.
Choice B: 20 pieces of meat and 32 pieces of vegetables.
Both 20 and 32 are multiples of 4. A valid option.
Choice C: 30 pieces of meat and 40 pieces of vegetables.
Both 30 and 40 are multiples of both 3 and 4. A valid option.
Choice D: 45 pieces of meat and 60 pieces of vegetables.
Both 45 and 60 are multiples of both 3 and 4. A valid option.
Choice E: 72 pieces of meat and 96 pieces of vegetables.
Both 72 and 96 are multiples of both 3 and 4. A valid option.
So, the valid options are Choices B, C, and E.