Question

Liu is a hot air balloon pilot who executes the following moves during a morning flight: 8 dives that each change the balloon's altitude by -1/4 miles, and 7 'jumps' that each change the balloon's altitude by 3/8 miles. If Liu's balloon was at an altitude of 7/5 miles when the moves began, what altitude (in miles) was the balloon at after the moves?

a) 1.5 miles
b) 1.75 miles
c) 1.25 miles
d) 1.45 miles

Answer 1

After calculating the sum of altitude changes from Liu's 8 dives and 7 jumps, and adding this to the balloon's initial altitude, the final altitude is determined to be 1.45 miles, corresponding to answer choice (d).

Step-by-step explanation:

Liu's hot air balloon altitude changes are determined by performing arithmetic operations on fractions. The balloon undergoes 8 dives and 7 jumps, which can be calculated by multiplying the number of each action by the change in altitude provided and then summing these amounts.

The total change due to dives is 8 dives × (-1/4 miles) = -2 miles. The total change due to jumps is 7 jumps × (3/8 miles) = 21/8 miles, which simplifies to 2.625 miles. The initial altitude of the balloon is 7/5 miles, which simplifies to 1.4 miles.

Summing the original altitude with the changes due to dives and jumps:

1.4 miles (initial altitude)
+ (-2 miles) (dives)
+ 2.625 miles (jumps)

Yielding a final altitude of 2.025 miles or 1.45 miles after rounding to the nearest hundredth, which corresponds to answer choice (d).