Difference between revisions of "2004 AMC 12A Problems/Problem 3"

Revision as of 19:14, 3 July 2013

For how many ordered pairs of positive integers $(x,y)$ is $x + 2y = 100$ ?

$\text {(A)} 33 \qquad \text {(B)} 49 \qquad \text {(C)} 50 \qquad \text {(D)} 99 \qquad \text {(E)}100$

Every integer value of $y$ leads to an integer solution for $x$ Since $y$ must be positive, $y\geq 1$

Also, $y = \frac{100-x}{2}$ Since $x$ must be positive, $y < 50$

$1 \leq y < 50$ This leaves $49$ values for y, which mean there are $49$ solutions to the equation $\Rightarrow \mathrm{(B)}$

2004 AMC 12A (Problems • Answer Key • Resources)
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All AMC 12 Problems and Solutions

Revision as of 14:44, 26 February 2008 (view source) Chickendude (talk \| contribs) (Clarified solution) ← Older edit		Revision as of 19:14, 3 July 2013 (view source) Nathan wailes (talk \| contribs) (→‎See Also) Newer edit →
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