Difference between revisions of "2009 AMC 10A Problems/Problem 7"

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<math>
 
<math>
\mathrm{(A)}\ \frac{12}{5} \qquad
+
\mathrm{(A)}\ \frac{12}{5}
\mathrm{(B)}\ 3 \qquad
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\qquad
\mathrm{(C)} \frac{10}{3} \qquad
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\mathrm{(B)}\ 3
\mathrm{(D)} 38 \qquad
+
\qquad
\mathrm{(E)} 42 \qquad
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\mathrm{(C)}\ \frac{10}{3}
 +
\qquad
 +
\mathrm{(D)}\ 38
 +
\qquad
 +
\mathrm{(E)}\ 42
 
</math>
 
</math>
  
 +
==Solution==
 +
Rewording the question, basically, we are being asked "<math>2</math> is <math>40%</math> less than what number?"
 +
If <math>x</math> represents the number we are looking for, then <math>40%</math> less than the number would be represented by <math>x-0.4x</math> or <math>0.6x</math>.
 +
Thus <math>0.6x=2</math>; solving for <math>x</math>, we get <math>x=\frac{10}{3}</math>, <math>\longrightarrow \fbox{C}</math>
  
==Solution==
+
==See also==
 +
{{AMC10 box|year=2009|ab=A|num-b=6|num-a=8}}
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{{MAA Notice}}

Revision as of 12:42, 18 April 2021

Problem

A carton contains milk that is $2$% fat, an amount that is $40$% less fat than the amount contained in a carton of whole milk. What is the percentage of fat in whole milk?

$\mathrm{(A)}\ \frac{12}{5} \qquad \mathrm{(B)}\ 3 \qquad \mathrm{(C)}\ \frac{10}{3} \qquad \mathrm{(D)}\ 38 \qquad \mathrm{(E)}\ 42$

Solution

Rewording the question, basically, we are being asked "$2$ is $40%$ (Error compiling LaTeX. ! Missing $ inserted.) less than what number?" If $x$ represents the number we are looking for, then $40%$ (Error compiling LaTeX. ! Missing $ inserted.) less than the number would be represented by $x-0.4x$ or $0.6x$. Thus $0.6x=2$; solving for $x$, we get $x=\frac{10}{3}$, $\longrightarrow \fbox{C}$

See also

2009 AMC 10A (ProblemsAnswer KeyResources)
Preceded by
Problem 6
Followed by
Problem 8
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
All AMC 10 Problems and Solutions

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