[Math] 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

algebra-precalculus

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?

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