If the price of coffee is raised by 25%, by what percentage a householder must reduce his consumption of coffee so as not increase his expenditure?
Price of the coffee is $x $ Expenditure is $y$ Consumption will be $xy$
Increased price of coffee is $1.25x$ Expenditure is y consumption will be $1.25xy$
Now what to do next?
Best Answer
Hint:
If $p$ is the old price and $q$ is the old consumption, the new consumption $x$ must be such that: $$ 1.25p \cdot x=p\cdot q $$
so: $x=...$
the percentage variation of consumption is: $$ \Delta( q)\% =\frac{x-q}{q} \cdot 100=\left(\frac{x}{q}-1 \right)\cdot 100 $$
with ( from the previous equation)
$$x=\frac{q}{1.25}$$
can you do this?