Difference between revisions of "2006 Cyprus MO/Lyceum/Problem 1"
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The quantity of milk with <math>1\%</math> fat, that was added is (in kg) | The quantity of milk with <math>1\%</math> fat, that was added is (in kg) | ||
− | + | <math>\mathrm{(A)}\ 1000\qquad\mathrm{(B)}\ 600\qquad\mathrm{(C)}\ 800\qquad\mathrm{(D)}\ 120\qquad\mathrm{(E)}\ 480</math> | |
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− | B | ||
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− | C | ||
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− | D | ||
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− | E | ||
==Solution== | ==Solution== | ||
− | Let <math>x</math> be the number of kg of | + | Let <math>x</math> be the number of kg of <math>4\%</math> milk and let <math>y</math> be the number of kg of <math>1\%</math> milk. |
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− | <math>\ | ||
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− | <math>x= | + | We then have the equations <math>x+y=1200</math> and <math>\frac{4x+y}{100}=1200*.02=24</math>. |
− | <math>y=1200-400=800 \Rightarrow \mathrm {(C)}</math> | + | Solving, we find <math>X=400</math>, and <math>y=1200-400=800\Rightarrow\mathrm{(C)}</math>. |
==See also== | ==See also== |
Latest revision as of 10:54, 27 April 2008
Problem
A diary industry, in a quantity of milk with fat adds a quantity of milk with fat and produces kg of milk with fat. The quantity of milk with fat, that was added is (in kg)
Solution
Let be the number of kg of milk and let be the number of kg of milk.
We then have the equations and .
Solving, we find , and .
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 |