I'll do the first two problems (13 and 14) to get you started.
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Problem 13
I'm going to use square blocks instead of marbles. The same idea applies either way. I'm using blocks because they are easier to draw out.
Draw 9 square blocks that are connected end-to-end forming a long chain. Write O in the first four blocks to represent "orange". Write G in the remaining 5 blocks to represent "green". See figure 1 in the attached image below.
This diagram represents the fact that the orange and green blocks form a ratio of 4:5. There are 4 parts that are orange and 5 parts that are green.
If we have 6 rows of these blocks (see figure 2), then we'll have 6*5 = 30 green blocks overall. This leads to 6*4 = 24 orange blocks. So far we have 30+24 = 54 blocks that are green or orange.
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Let x be the total number of blocks
40% of the total x is the number of yellow
40% of x = 0.40*x
60% of x is the remaining number
0.60*x = 54
x = 54/0.60
x = 90
There are 90 blocks total
40% of 90 = 0.40*90 = 36 are yellow
60% of 90 = 0.60*90 = 54 are either green or orange
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Final Answer: 36 yellow marbles
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Problem 14
Michael has 40 books. Susan has 50% more books than Michael. This means she has 1.5 times as many books
1.5*40 = 60
Susan has 60 books
If Michael buys 8 more books, then he will have 40+8 = 48, which is still less than 60. Susan still has more books.
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Let's compute the percentage difference
A = 48 is the amount of books Michael has
B = 60 is the amount Susan has
C = percent difference
C = 100*(B-A)/A
C = 100*(60-48)/48
C = 25%
Susan has 25% more books compared to Michael
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Final Answer: Susan will still have more books. She will have 25% more books after Michael buys those 8 books.
