1) An elevator goes down 7 floors, up 3 floors, up 6 floors, down 8 floors, up 1 floor, and down 6 floors. It is now on floor 3. Which floor did it start on?
2) Megan bought a book for $12.00, received an allowance of $15.00, paid back a loan of $7.00, bought lunch for $8.50,earned $8.00 raking leaves, and found $2.00. She now has $22.25. How much did she start with?
3) Miguel and Yoshi went rock climbing. Miguel climbed up 15m, back down 4m, climbed 6m,slid back 17m, climbed up 22m, rested and climbed 14m more. Yoshi climbed 12m, slid back 4m, rested, climbed up 33m and slid back 7m. They are now together at the 40m mark. At what level did each start climbing?
4) Shailini's plane leaves at 3:35 P.M. She has to check in 2 h before take-off. She takes 1 h and 35 min to get to the airport from her home. Shailini must first drop off her dog, Fido, at her friend's house next door. She wants to spend 45 min talking to her friend.What is the latest time she should leave her house?
Set-up equations
1) x - 7 + 3 + 6 - 8 + 1 - 6 = 3
x + 10 - 21 = 3
x - 11 = 3
x = 13
2) x - 12.00 + 15.00 - 7.00 - 8.50 + 8.00
+ 2.00 = 22.25
You solve
3)
Miguel
x + 15 - 4 + 6 - 17 + 22 + 14 = 40
Yoshi
x + 12 - 4 + 33 - 7 = 40
You solve
4)
3:35--plane
2:00--less 2h
1:35--check-in
1:35--less to get to airport
12:00--noon
00:45--less 45 min talking
11:15--leave house
Check for this
11:15---leave house
00:45---45 min talking
12:00---time now
1:35---1 hr 35 min trip to airport
1:35---time now at airport
2:00---2 hrs early for check-in
3:35---time now--
plane leaves
I think in a question 2 the answer is 24.75. Correct?
What about a question 4. 3:35 is the latest time she should leave her house?
I’m doing the same questions in 2019
My teacher just gave me these questions today! it's 2020 quarentine lol
1) To determine the starting floor of the elevator, we need to track its movements.
Let's start with the elevator on floor X. It goes down 7 floors, so it will be on floor X - 7.
Then it goes up 3 floors, resulting in floor (X - 7) + 3 = X - 4.
Next, it goes up 6 floors, resulting in floor (X - 4) + 6 = X + 2.
Afterwards, it goes down 8 floors, resulting in floor (X + 2) - 8 = X - 6.
Then it goes up 1 floor, resulting in floor (X - 6) + 1 = X - 5.
Finally, it goes down 6 floors, resulting in floor (X - 5) - 6 = X - 11.
Given that the elevator is now on floor 3, we can set up the equation X - 11 = 3.
Solving for X, we find X = 14.
Therefore, the elevator started on the 14th floor.
2) We need to find out Megan's starting amount by tracking the transactions.
Let's say Megan started with an unknown amount, X.
She bought a book for $12.00, so she then had X - 12.
Megan received an allowance of $15.00, which added to her balance of (X - 12) + 15 = X + 3.
She paid back a loan of $7.00, leaving her with (X + 3) - 7 = X - 4.
After buying lunch for $8.50, she had (X - 4) - 8.50 = X - 12.50.
Then, she earned $8.00 raking leaves, resulting in (X - 12.50) + 8 = X - 4.50.
Finally, Megan found $2.00, resulting in X - 4.50 + 2 = X - 2.50.
Given that Megan now has $22.25, we can set up the equation X - 2.50 = 22.25.
Solving for X, we find X = 24.75.
Therefore, Megan started with $24.75.
3) To determine at what level Miguel and Yoshi started climbing, we will track their ascents and descents.
Let's say Miguel started climbing at level X and Yoshi started climbing at level Y.
Miguel climbed up 15m, so he was at level X + 15.
He then climbed back down 4m, putting him at level (X + 15) - 4 = X + 11.
Next, Miguel climbed 6m, resulting in level (X + 11) + 6 = X + 17.
He then slid back 17m, putting him at level (X + 17) - 17 = X.
Miguel then climbed up 22m, resulting in level X + 22.
After resting, Miguel climbed 14m more, resulting in level (X + 22) + 14 = X + 36.
Yoshi climbed 12m, putting him at level Y + 12.
He then slid back 4m, resulting in level (Y + 12) - 4 = Y + 8.
After resting, Yoshi climbed up 33m, resulting in level (Y + 8) + 33 = Y + 41.
Yoshi then slid back 7m, putting him at level (Y + 41) - 7 = Y + 34.
The equation we can set up is X + 36 + Y + 34 = 40 (since they are together at the 40m mark).
Simplifying, we have X + Y = -30.
Given that the levels climbed must be positive integers, we need to find two integers X and Y that satisfy the equation X + Y = -30. This is impossible, as the sum of two positive integers cannot be negative.
Therefore, there is no solution where both Miguel and Yoshi start at positive levels.
4) To determine the latest time Shailini should leave her house, we need to add up the time required for each task.
Shailini's plane leaves at 3:35 P.M., and she must check in 2 hours before take-off. This means she needs to be at the airport by 1:35 P.M.
She takes 1 hour and 35 minutes to get to the airport from her home. We can convert this to hours, which equals 1.58 hours.
Shailini also wants to spend 45 minutes talking to her friend before leaving.
To find the latest time she should leave her house, we can subtract the total time required (2 hours for check-in + 1.58 hours for the trip + 0.75 hours for talking) from the desired arrival time.
1:35 P.M. - (2 hours + 1.58 hours + 0.75 hours) = 1:35 P.M. - 4.33 hours = 9:02 A.M.
Therefore, the latest time Shailini should leave her house is 9:02 A.M.