Question

A family is using Liquefied petroleum gas (LPG) of weight 14.2 kg for consumption. (Full weight 29.5kg includes the empty cylinders tare weight of 15.3kg.). If it is used with constant rate then it lasts for 24 days. Then the new cylinder is replaced. Find the equation relating the quantity of gas in the cylinder to the days

Answer 1

Find the equation relating the quantity of gas in the cylinder to the days.

Given Total weight of cylinder = 29.5 kg

Weight of the gas inside the cylinder = 14.2 kg

Let x denote the number of days of consumption of the gas, y denote the quantity of gas inside a cylinder.

Initially x = 0 then y = 14.2

The corresponding point is (0, 14.2)

The gas inside the cylinder lasts for 24 days

∴ When x = 24

We have y = 0

The corresponding point is (24, 0)

∴ The linear relation between the quantity of gas in the cylinder to the number of days of consumption is the equation of the line joining the points (0, 14.2) and (24, 0).

`(x - 0)/(24 - 0) = (y - 14.2)/(0 - 14.2)`

`x/24 = (y - 14.2)/(- 14.2)`

y – 14.2 = `- 14.2 xx x/24`

y = `(- 14.2)/24 x + 14.2`

y = `- 142/240 x + 14.2`

y = `- 71/120 x + 14.2`

0 ≤ x ≤ 24

which is the required relation