Difference between revisions of "2006 Cyprus MO/Lyceum/Problem 1"
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==Problem== | ==Problem== | ||
| + | A diary industry, in a quantity of milk with <math>4\%</math> fat adds a quantity of milk with <math>1\%</math> fat and produces <math>1200</math>kg of milk with <math>2\%</math> fat. | ||
| + | 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> | ||
==Solution== | ==Solution== | ||
| − | {{ | + | 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. |
| + | |||
| + | We then have the equations <math>x+y=1200</math> and <math>\frac{4x+y}{100}=1200*.02=24</math>. | ||
| + | |||
| + | Solving, we find <math>X=400</math>, and <math>y=1200-400=800\Rightarrow\mathrm{(C)}</math>. | ||
==See also== | ==See also== | ||
{{CYMO box|year=2006|l=Lyceum|before=First Question|num-a=2}} | {{CYMO box|year=2006|l=Lyceum|before=First Question|num-a=2}} | ||
| + | |||
| + | [[Category:Introductory Algebra Problems]] | ||
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 | ||
