Maggie has a box of 200 colored blocks. The box has an equal number of green and blue blocks and an equal number of red and yellow blocks. If Maggie arranged all of the green blocks in stacks of 10 and all of the blue blocks in stacks of 7, how many yellow blocks are in the box?
If g and b are the number of stacks, then
10g = 7b
LCM(7,10) = 70
So, the smallest number of blocks would be
70 green and 70 blue, leaving 60 red and yellow blocks.
So, 30 of them are yellow.
Could there be more green/blue? No, since that would require at least 280 blocks.
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even tho u answerd this 3 years ago
damn
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A florist has 64 red balloons and 48 blue balloons. What is the greatest number of identical balloon bouquets that can be made without any balloons leftover?
Responses
A 1212
B 1616
C 88
D 1818
The greatest number of identical balloon bouquets that can be made without any balloons leftover is the greatest common factor (GCF) of 64 and 48.
To find the GCF, we can list the factors of each number:
Factors of 64: 1, 2, 4, 8, 16, 32, 64
Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
The common factors are 1, 2, 4, 8, and 16. The greatest common factor is 16.
Therefore, the answer is B) 16.
Pencils are sold 9 to a package, and pens are sold 6 to a package. If an equal number of pencils and pens are purchased, what is the minimum number of each item?
Responses
A 1818
B 2828
C 3636
D 54
For the minimum number of each item, we need to find the least common multiple (LCM) of 9 and 6, which is 18. Each package of pencils contains 9 pencils, which is twice the number of packages of pens, since each package of pens contains 6 pens.
So, if x is the number of packages of pens, then the number of packages of pencils is 2x. We want an equal number of pencils and pens, so we must have:
2x = x
which means:
x = 0
This is not possible, so we must increase the number of packages of pencils and pens by a common factor until we get to a valid solution.
Let's try:
2 packages of pencils (18 pencils)
1 package of pens (6 pens)
This gives us equal numbers of pencils and pens (18 pencils and 6 pens).
Therefore, the minimum number of each item is 2 packages of pencils and 1 package of pens, or a total of 18 pencils and 6 pens.
The answer is not listed in the choices given, so it may be a mistake or incomplete.