Difference between revisions of "2007 iTest Problems/Problem 2"

Revision as of 14:22, 11 December 2007

Problem

Find $a + b$ if $a$ and $b$ satisfy $3a + 7b = 1977$ and $5a + b = 2007$ .

$\mathrm{(A)}\, 488\quad\mathrm{(B)}\, 498$

Solution

$3a + 7b = 1977$ and $5a + b = 2007$ .

Thus, $b=2007-5a$ , and substituting, $3a+14049-35a=1977\Rightarrow -32a=-12072\Rightarrow a=377.25$ . Thus, $b=2007-1886.25\Rightarrow b=120.75$ . Thus, $a+b=377.25+120.75=498\Rightarrow \boxed{\mathrm{B}}$

2007 iTest (Problems, Answer Key)
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Difference between revisions of "2007 iTest Problems/Problem 2"

Revision as of 14:22, 11 December 2007

Problem

Solution