Question

1. one month, a homeowner used 150 units of gas and 520 units of electric for a total cost of $84.20. the next month, 210 units of gas and 405 units of electric were used for a total cost of $82.35. find the cost per unit of gas and electric.

Explanation:

Step1: Let cost per unit of gas be $x$ and cost per unit of electric be $y$.

Set up equations based on given data:
$150x + 520y=84.20$ (Equation 1)
$210x + 405y=82.35$ (Equation 2)

Step2: Multiply Equation 1 by 7 and Equation 2 by 5 to make coefficients of $x$ equal.

Equation 1 becomes $1050x+3640y = 589.4$
Equation 2 becomes $1050x+2025y = 411.75$

Step3: Subtract the new - formed Equation 2 from new - formed Equation 1 to eliminate $x$.

$(1050x + 3640y)-(1050x + 2025y)=589.4 - 411.75$
$1050x+3640y - 1050x - 2025y=177.65$
$1615y=177.65$
$y=\frac{177.65}{1615}=0.11$

Step4: Substitute $y = 0.11$ into Equation 1 to find $x$.

$150x+520\times0.11 = 84.20$
$150x+57.2=84.20$
$150x=84.20 - 57.2$
$150x=27$
$x=\frac{27}{150}=0.18$

Answer:

The cost per unit of gas is $0.18$ and the cost per unit of electric is $0.11$.