Grace uses the formula \(A = \frac{h(x + y)}{2}\) to estimate her average monthly running cost for the household, a method she picked up from a budgeting co...
Question 1 Report
Grace uses the formula \(A = \frac{h(x + y)}{2}\) to estimate her average monthly running cost for the household, a method she picked up from a budgeting course she attended last spring, where \(A\) is the average, \(h\) is a fixed weighting she chose herself, and \(x\) and \(y\) are two months' costs.
- Make \(y\) the subject of the formula (3)
Answer Details
This question tests rearranging a formula containing a fraction and two variables added together to make one of them the subject.
Starting from \(A=\frac{h(x+y)}{2}\), multiply both sides by \(2\) to clear the fraction:
\[2A=h(x+y)\]Divide both sides by \(h\) to isolate the bracket:
\[\frac{2A}{h}=x+y\]Finally, subtract \(x\) from both sides to isolate \(y\):
\[y=\frac{2A}{h}-x\][3] (1 for clearing the fraction, 1 for dividing by \(h\), 1 for the fully correct final formula)
The bracket \((x+y)\) must be treated as a single quantity until the very last step; dividing by \(h\) before clearing the \(2\) or before removing the bracket would introduce fractions inside fractions and is a common source of error.
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