Question

Karina uses the system of equations below to compare the monthly utility costs in July and December for electricity, x, and natural gas, y.

750x + 17y = 141.61
300x + 30y = 75.90
Karina solves the system using linear combination and arrives at the equation 116y = 96.28. She then solves this equation for y. Which statement explains Karina’s solution?

The cost of natural gas is $0.17 per unit.
The cost of natural gas is $0.20 per unit.
The cost of natural gas is $0.72 per unit.
The cost of natural gas is $0.83 per unit.

Answer 1

To determine which statement explains Karina's solution, we can analyze the equation she derived:

\[ 116y = 96.28 \]

To solve for \( y \), we divide both sides of the equation by 116:

\[
y = \frac{96.28}{116}
\]

Calculating this gives:

\[
y = 0.83
\]

Now, we interpret this in the context of the problem. The variable \( y \) represents the cost of natural gas per unit. Therefore, since \( y \approx 0.83 \), we conclude that:

**The cost of natural gas is $0.83 per unit.**

Thus, the correct explanation for Karina's solution is:

**The cost of natural gas is $0.83 per unit.**