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# Advanced Math/Word problem

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Question
A householder buys gas and electricity from the same supplier and pays only for the units of gas and electricity used.

One unit of electricity costs three times as much as one unit of gas.

In one year, the householder uses 20100 units of gas and 3300 units of electricity. The householder's total combined fuel bill for one year is £750.

(Use the symbol g to represent the cost of one unit of gas and e electricity)

The supplier warns that the cost of gas and electricity may rise but it offers customers a Fixed Price Deal. The supplier explains

'Under the Fixed Price Deal, we will keep the cost of gas and electricity fixed at present prices for two years provided customers make an additional monthly payment of £2.50.'

The householder can choose to take the Fixed Price Deal or agree to pay any price increases that may occur over the two years. The householder plans to use the same amount of gas and electricity in each of the next two years.

What percentage increase in her total fuel bill of £1500 over the next two years has to be exceeded before she will pay more than she would with the Fixed Price Deal?

from my work out I know that g = e/3 or e = 3g from this 30000g = 750 or
20100g + 3300e = 750 and a unit of g = £ 0.025  and a unit of e = £ 0.075.
However, I couldn't figure it out the above question. PS help
thanks
Aba

Answer
"The fuel bill for one year is £750."
Two-year fuel bill at current prices = £1500

"Fixed-Price Deal:  the cost per unit stays constant for two years, for an additional monthly payment of £2.50"
24 months × £2.50/month = £60

£60/£1500 = 0.04
The break-even point is a 4% increase in her two-year bill. If fuel prices increase by more than 4%, she will be paying more than she would under the Fixed-Price Deal.
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