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Solution |
1) Leena is descending a flight of stairs. She is one-fifth the way down. If she takes 28 more steps, she will be one-third the way down. How many steps are in the flight of stairs?
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Let s = the number of steps in the flight of stairs.
- 28 steps + 1⁄5 of the flight of stairs = 1⁄3 of the flight
28 + 1⁄5 s = 1⁄3 x
s (1⁄3 - 1⁄5) = 28
s (5⁄15 - 3⁄15) = 28
2⁄15 s = 28
s = (28 x 15) / 2 = 210 steps
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2) The table shows data on the sales of specialty cakes at a local bakery. Assuming the data is linear, what is the price for 12 cakes?
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- With the number of cakes as the x axis and their price as y, find the slope of the linear equation using the first 2 points:
(63.5 - 34.5) / (7 - 3) = 29/4 = $7.25/cake
- Apply this slope to the 12 cake value using the 7 cake data:
y = $63.5 + $7.25 x (12-7) = $63.5 + $7.25 x 5 = $99.75
Note: You could also have used either of the other 2 points. For example using the first point:
y = $34.50 + $7.25 x (12-3) = $34.50 + $7.25 x 9 = $99.75
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3) Your friend asks for your help with her project because they know you could finish it in half the time it would take them. Without your help, it would take your friends 30 days to finish the project. Working together, how long will it take to finish the project?
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- Your friend works at a rate of 30 days/project
- You work at a rate of 15 days/project
- Let d = the number of days you work together to accomplish the project.
- Then (d/30 + d/15) = 1 project
(d/30 + 2d/30) = 1
3d = 30
d = 10 days
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