SOLUTION: During one month, a homeowner used 200 units of electricity and 110 units of gas for a total of $79.00. The next month, 230 units of electricity and 250 units of gas were used for

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Question 332541: During one month, a homeowner used 200 units of electricity and 110 units of gas for a total of $79.00. The next month, 230 units of electricity and 250 units of gas were used for a total of $103.20. Find the cost per unit of gas.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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a homeowner used 200 units of electricity and 110 units of gas for a total of $79.00.
The next month, 230 units of electricity and 250 units of gas were used for a total of $103.20.
Find the cost per unit of gas.
:
x = cost per unit of electricity
g = cost per unit of gas
:
Substitution using decimals will involve the least work here
:
Write a cost equation for each month
:
Month one
200x + 110g = 79
200x = 79 - 110g
Divide both sides by 200, results
x = (.395 - .55g)
:
month two
230x + 250g = 103.20
:
replace x with (.395-.55g)
230(.395-.55g) + 250g = 103.2
90.85 - 126.5g + 250g = 103.2
250g - 126.5g = 103.2 - 90.85
123.5g = 12.35
g = 12.35%2F123.5
g = $.10 per unit of gas
:
:
In order to check our solution we have to find the cost of x
x = .395 - .55(.10)
x = .395 = .055
x = $.34 per unit of elec
:
Check using these values in the 2nd month equation
230(.34) + 250(.10) =
78.2 + 25 = 103.20, confirms our solution