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Solution |
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1) Larry tells his friend he has a bag containing 4 types of marbles: cat's eye, clear, cloud, and corkscrew. He says that 1/9 of the marbles are corkscrew, 2/9 are clear, and 5 are cloud. What is the fewest number of cat's eye marbles that could be in the bag? |
1. Corkscrew and clear marbles account for
(1/9 + 2/9) = 3/9 = 1/3 of the marbles.
2. Cloud and cat's eye marbles account for 2/3 of the marbles.
3. Since there must be a whole number of cat's eye marbles, compute the minimum number of them that would allow them and cloud marbles to be 2/3 of the whole = 1 cloud marble.
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2) Mira's friend is having a birthday this month, but Mira always forgets the exact date. Mira's friend reminds her that 1/3 of the birth date plus 52 equals two times as much as the birth date. What day is her friend's birthday?
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Let D be the birth date.
Solve the equation (1/3)D + 25 = 2 D.
D/3 + 25 = 2D
2D - D/3 = 25
5/3 D = 25
D = 75/5 = 15
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3) A group of friends are renting a bus to attend a convention. The company charges a flat rate for a rental, regardless of the number of people using the bus. Fifteen people are planning on attending and want to split the cost evenly. If they get 9 more people they can reduce the cost of the rental by $4.50 per person. How much does it cost to rent the bus? |
Let C = the cost of the bus.
1. Then C/15 is the cost per person for 15 people
2. C/24 is the cost per person for 24 people
3. Write an equation for "the cost per person for 15 people is the cost per person for 24 people plus $4.50" and solve.
C/15 = C/24 + $4.50
C(1/15 - 1/24) = $4.50
C(24/360 - 15/360) = $4.50
C(9/360) = $4.50
C = 40 X $4.50 = $180
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