SOLUTION: During one month, a homeowner used 700 units of electricity and 100 units of gas for a total cost of $486. The next month, 500 units of electricity and 250 units of gas were used f

Question 1184064: During one month, a homeowner used 700 units of electricity and 100 units of gas for a total cost of $486. The next month, 500 units of electricity and 250 units of gas were used for a total cost of $415. Find the cost per unit of gas.

Answer by CPhill(1959) (Show Source): You can put this solution on YOUR website!
Here's how to solve this problem:
**Let:**
* 'e' be the cost per unit of electricity.
* 'g' be the cost per unit of gas.
**Set up the equations:**
* **Equation 1 (Month 1):** 700e + 100g = 486
* **Equation 2 (Month 2):** 500e + 250g = 415
**Solve the equations:**
One way to solve this is using elimination:
1. **Multiply Equation 1 by 2.5:**
1750e + 250g = 1215
2. **Subtract Equation 2 from the modified Equation 1:**
(1750e + 250g) - (500e + 250g) = 1215 - 415
1250e = 800
3. **Solve for e:**
e = 800 / 1250
e = 0.64
4. **Substitute the value of e back into either Equation 1 or 2 to solve for g. Let's use Equation 1:**
700(0.64) + 100g = 486
448 + 100g = 486
100g = 38
g = 0.38
**Answer:**
The cost per unit of gas is $0.38.

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