Art of Problem Solving
Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

2006 Cyprus MO/Lyceum/Problem 1: Difference between revisions

← Older edit
m cat
I like pie (talk | contribs)
747 edits
Standardized answer choices; minor edits
 
Line 3: Line 3:
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)


A. <math>1000</math>
<math>\mathrm{(A)}\ 1000\qquad\mathrm{(B)}\ 600\qquad\mathrm{(C)}\ 800\qquad\mathrm{(D)}\ 120\qquad\mathrm{(E)}\ 480</math>
 
B. <math>600</math>
 
C.  <math>800</math>
 
D. <math>120</math>
 
E. <math>480</math>


==Solution==
==Solution==
Let <math>x</math> be the number of kg of 4% milk and let y be the number of kg of 1% milk. We then have the equations
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.
 
<math>x+y=1200</math>
 
<math>\dfrac{4x+y}{100}=1200*.02=24</math>
 
<math>4x+y=2400</math>
 
<math>3x=1200</math>


<math>x=400</math>
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 09:54, 27 April 2008

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
Retrieved from "https://wiki.aopstest.com/wiki/index.php?title=2006_Cyprus_MO/Lyceum/Problem_1&oldid=25609"