2006 Cyprus MO/Lyceum/Problem 1

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Problem

A diary industry, in a quantity of milk with $4\%$ fat adds a quantity of milk with $1\%$ fat and produces $1200$ kg of milk with $2\%$ fat. The quantity of milk with $1\%$ fat, that was added is (in kg)

$\mathrm{(A)}\ 1000\qquad\mathrm{(B)}\ 600\qquad\mathrm{(C)}\ 800\qquad\mathrm{(D)}\ 120\qquad\mathrm{(E)}\ 480$

Solution

Let $x$ be the number of kg of $4\%$ milk and let $y$ be the number of kg of $1\%$ milk.

We then have the equations $x+y=1200$ and $\frac{4x+y}{100}=1200*.02=24$ .

Solving, we find $X=400$ , and $y=1200-400=800\Rightarrow\mathrm{(C)}$ .

2006 Cyprus MO, Lyceum (Problems)
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2006 Cyprus MO/Lyceum/Problem 1

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