Question

Liu is a hot air balloon pilot. If the balloon's initial altitude was

7
5
5
7
​
miles, and Liu executes 8 dives decreasing altitude by
−
1
4
−
4
1
​
miles each and 7 'jumps' increasing altitude by
3
8
8
3
​
miles each, what is the final altitude of the balloon?

a.
7
5
5
7
​
miles
b.
13
10
10
13
​
miles
c.
23
20
20
23
​
miles
d.
33
20
20
33
​
miles

Answer 1

The final altitude of Liu's balloon after 8 dives and 7 jumps is 7557₃⁄₈ miles, which matches option (d) 33202033⁄₈ miles.

Step-by-step explanation:

The initial altitude of the balloon is given as 7557 miles. Liu performs 8 dives, each decreasing the altitude by −4⁄₁ miles, and 7 jumps, each increasing the altitude by ⅜³ miles. To find the final altitude, we calculate the total change in altitude from the dives and jumps and add that to the initial altitude.

First, we calculate the total altitude loss from the dives: 8 dives × (−4⁄₁ miles) = −₁¹⁄₈ miles. Then we calculate the total altitude gain from the jumps: 7 jumps × (⅜³ miles) = ₂²⁄₇ miles. Adding these together, we get the total altitude change: (−₁¹⁄₈ miles) + (₂²⁄₇ miles) = (₂₂ − ₁₉)⁄₈ miles, which simplifies to ₃⁄₈ miles.

Finally, we add the total change in altitude to the initial altitude: 7557 miles + ₃⁄₈ miles = 7557₃⁄₈ miles. Thus, the final altitude of the balloon is 7557₃⁄₈ miles, which corresponds to option (d) 33202033⁄₈ miles.