Problem Solving

Hello BTG
How do we best approach this problem?

A rainstorm increased the amount of water stored in State J reservoirs from 124 billion gallons to 138 billion gallons. If the storm increased the amount of water in the reservoirs to 82 percent of the total capacity, approximately how many billions gallons of water were the reservoirs short of total capacity prior to the storm?

a) 9
b) 14
c) 25
d) 30
e) 44

Thanks in advance [/spoiler]

lucas211 wrote:Hello BTG
How do we best approach this problem?

A rainstorm increased the amount of water stored in State J reservoirs from 124 billion gallons to 138 billion gallons. If the storm increased the amount of water in the reservoirs to 82 percent of the total capacity, approximately how many billions gallons of water were the reservoirs short of total capacity prior to the storm?

a) 9
b) 14
c) 25
d) 30
e) 44

Thanks in advance

So 138 billion gallons is 82% of total capacity.

I see that the answer choices are pretty far apart. So let's just round and say that 136 billion gallons is 80% of total capacity.

136 = 4/5 of total capacity. 136/4 = 100/4 + 36/4 = 25 + 9 = 34 (Might as well do it in my head.)

Ok, 34 should be close enough.

Total Capacity = 34 x 5 = 170

Difference Before Storm 170 - 124 = 46.

Ok. So that's closest to 44, and the correct answer is E.

lucas211 wrote:Hello BTG
How do we best approach this problem?

A rainstorm increased the amount of water stored in State J reservoirs from 124 billion gallons to 138 billion gallons. If the storm increased the amount of water in the reservoirs to 82 percent of the total capacity, approximately how many billions gallons of water were the reservoirs short of total capacity prior to the storm?

a) 9
b) 14
c) 25
d) 30
e) 44

Thanks in advance [/spoiler]

Assume the total capacity = 100x billion gallons
Given that 138 billion gallons = 82x

x = 138/82 = 1.68
Total water = 168 billion gallons
Initial water level was 168 - 124 = 44 billion gallons short of the capacity

Correct Option: E

We can also approximate the values to get the answer approximately.
x = 138/82 = 140/80 = 1.7 (Note that since we have increased the numerator and decreased the denominator, the final value will be larger)
Total water = 170 billion gallons
Difference = 170 - 124 = 46 billion gallons.
Only option E is the closest.