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2) Eugene and Florence are both reading books and they read for 20 minutes a day during an after school program that runs Monday through Friday.
Eugene reads 3 pages every 6 minutes and Florence reads 2 pages every 5 minutes.
If it takes Eugene 4 whole weeks to finish his book, and Florence takes 6 whole weeks, whose book is longer and by how many pages?
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1. Determine the amount of time Eugene reads by multiplying the amount of reading time per day times the number of days.
Eugene's reading time =
20 min X 5 days per week X 4 weeks = 400 minutes.
2. Florence's reading time =
20 min X 5 days per week X 6 weeks = 600 minutes.
3. Multiply each student's reading time by their reading rate to get their total number of pages read:
Eugene = 400 minutes x 3 pages/6 minutes = 200 pages.
Florence = 600 minutes x 2 pages/5 minutes = 240 pages.
4. Subtract the longer book length from the shorter book length to get how much longer the longer book is: Florence's book which has 40 more pages.
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3) A room is 25% full. If 900 more people enter the room it will be at full capacity. Full capacity is determined by one person per 1.5 square meters. The length of the room is 60 meters. What is the width of the room?
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1. If the room is 25% full and 900 more people enter it and it becomes full, then the 900 people must be 75% of the room's capacity.
2. Given that percentage, compute the room's capacity:
900 = 3/4, so 1/4 = 300 and 4/4 = 1200 people.
3. At one person per 1.5 square meters, the room's area is
1200 x 1.5 = 1800 sq. meters.
4. If the room is 60 meters wide, then to have this area the length must be 1800/60 = 30 meters.
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4) Aleisha is exercising her business talents as the go to classmate to get things from. She trades:
- 2 bags of chips = 1 candy bar
- 1 bag of chips = 5 pencils
- 3 pencils = 2 gel pens
How many gel pens can she get for 1 candy bar?
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Work backwards:
1. If 3 pencils = 2 gel pens, then 1 pencil = 2/3 gel pen.
2. If 1 bag of chips = 5 pencils, then 1 bag of chips =
5 x 2/3 gel pens/pencil = 3.33 gel pens.
3. If 1 candy bar = 2 bags of chips, then 1 candy bar =
2 x 3.33 = 6.667 gel pens.
Rounding down to 6 gel pens for 1 candy bar.
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5) In this diagram the two white triangles have height 7 cm and are congruent
What is the area of the dark parallelogram?
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"Congruent" means the 2 white triangles are the same size.
Method 1: Compute areas of triangles and subtract:
1. Compute the area of the outer rectangle = 12 x 4 = 48 sq. cm.
2. Compute the area of one white triangle = (4 x 7)/2 = 14 sq. cm.
3. Subtract the white areas from the outer rectangle area to get the area of the parallelogram = 48 - 14 - 14 = 20 sq. cm.
Method 2: Compute area of parallelogram:
1. Subtract height of a triangle from the length of the rectangle to get the width of the parallelogram = 12 - 7 = 5 cm.
2. Compute the area as base (4) times this height =
4 x 5 = 20 sq. cm.
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