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)

A. $1000$

B. $600$

C. $800$

D. $120$

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

$x+y=1200$

$\dfrac{4x+y}{100}=1200*.02=24$

$4x+y=2400$

$3x=1200$

$x=400$

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

See also

2006 Cyprus MO, Lyceum (Problems)
Preceded by
First Question
Followed by
Problem 2
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