Question

in a coastal town, the humidity, measured in grams of water per kilogram of air, increases by 43% for every 1 degree Celsius increase in temperature. A scientist observed that the humidity on monday morning 5.75 grams per kilogram. He wants to know how much the temperate must increase for the humidity to reach at least 49.17 grams per kilogram. Let T represent the increase in temperature, in degrees celsius, from monday mornings observation. Write an inequality to represent the situation, and use it to determine the desired temperature increase. a) T<2 b) T>8 c) T>6 d) T<4

Answer 1

Answer: Option 'C' is correct.

Explanation:

Since we have given that

Humidity on Monday morning = 5.75 grams per kilogram

Let T be the increase in temperature, in degrees celsius, from monday morning.

So, According to question, we have the humidity measured in grams of water per kilogram of air, increases by 43% for every 1 degree Celsius increase in temperature.

1) Rate of increment is 43% So, it becomes

`100+43=143\%\\\\143\%=(143)/(100)=1.43`

2) 43% increases for every 1 degree celsius.

`1.43* T`

So, it becomes,

`(100+43)/(100)* T\geq (49.17)/(5.75)\\\\(143)/(100)* T\geq 8.55\\\\T\geq (8.55* 100)/(143)\\\\T\geq 5.97\\\\T>6`

Hence, Option 'C' is correct.