2009 AMC 10A Problems/Problem 7

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

Solution 2

If we change the question to 2% fat in the carton which is 50% less than whole milk, this means that there is 4% fat in the whole milk. The only answer closest and less than 4 is 10/3, our answer. 38% fat is a lot of fat in milk :O -RealityWrites

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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