2006 Cyprus MO/Lyceum/Problem 1

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 $y=1200-400=800\Rightarrow\mathrm{(C)}$.

See also

2006 Cyprus MO, Lyceum (Problems)
Preceded by
First Question
Followed by
Problem 2
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Invalid username
Login to AoPS