Question

During one month, a homeowner used 600 units of electricity and 100 units of gas for a total cost of 390. The next month, 400 units of electricity and 250 units of gas were used for a total cost of $326. Find the cost per unit of gas.

Answer 1

cost per unit of gas i.e y= 0.36

Explanation:

Let cost per unit of electricity = x

and cost per unit of gas = y

The equations required will be:

`600x+100y=390 ---- eq(1)\\400x+250y=326----eq(2)`

We need to find value of y i.e cost per unit of gas

Solving equations to find value of y

We will use elimination method

Multiply equation 1 by 4 and 2 by 6

`2400x+400y=1560 ---- eq(1)\\2400x+1500y=1956----eq(2)`

Subtracting eq 1 from eq 2

`2400x+1500y=1956----eq(2)\\2400x+400y=1560 ---- eq(1)\\- \ \ \ \ \ - \ \ \ \ \ \ \ \ \ \ -\\----------------\\1100y=396\\y=(396)/(1100)\\y=0.36`

Solving we get y=0.36

Putting value of y in eq(1) to find value of x

`600x+100y=390\\600x+100(0.36)=390\\600x+36=390\\600x=390-36\\600x=354\\x=(354)/(600)\\x=0.59`

Value of x = 0.59

But we need to find only cost of unit of gas i.e y

So, cost per unit of gas i,e y= 0.36