Grace pays a fixed monthly charge of \(\pounds x\) for her household electricity supply, agreed when she first switched provider two winters ago, and a sepa...
Question 1 Report
Grace pays a fixed monthly charge of \(\pounds x\) for her household electricity supply, agreed when she first switched provider two winters ago, and a separate usage charge that is \(\pounds 8\) less than double the fixed charge. Her total monthly electricity bill comes to \(\pounds 61\) once both charges are added together.
- Set up an equation in \(x\) linking the two charges, then solve it (4)
- Give the usage charge for that month (1)
Answer Details
This question tests forming and solving a linear equation from a description of two related charges, then using the result to find one of the original quantities.
(a) The fixed charge is \(x\), and the usage charge is \(\pounds8\) less than double the fixed charge, so it is \(2x-8\). The two charges total \(\pounds61\):
\[x+(2x-8)=61\]Combine like terms:
\[3x-8=61 \quad\Rightarrow\quad 3x=69 \quad\Rightarrow\quad x=23\]The fixed charge is \(\pounds23\). [4] (1 for the correct equation, 1 for combining to \(3x-8=61\), 1 for isolating \(3x=69\), 1 for \(x=23\))
(b) Substitute \(x=23\) into the usage-charge expression:
\[2(23)-8=46-8=38\]The usage charge for that month is \(\pounds38\). [1]
Checking the answer by adding the two charges, \(23+38=61\), confirms both the fixed charge and the usage charge are consistent with the total bill given, which is good practice whenever a problem asks for a second value derived from the first.
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