Question 130734
Angles are complementary if and only if the sum of their measures is 90 degrees.  If the two angles have degree measures of p and 3p - 6, then:


{{{p + 3p - 6 = 90}}}
{{{4p-6=90}}}
{{{4p=96}}}
{{{p=24}}}


Check:
{{{3*24-6=72-6=66}}}.
{{{66+24=90}}} Answer checks.


If x is an even integer, the next consecutive even integer is x + 2  (that's because x + 1 would be odd).  Their sum is 450, so {{{x + (x + 2)=450}}}


{{{2x+2=450}}}
{{{2x=448}}}
{{{x=224}}}


Check:
{{{224 + 226 = 450}}} Answer checks.


The perimeter of a rectangle is {{{P=2L + 2W}}}, but we are given that {{{L=W+50}}} and {{{P=500}}}, so:


{{{2(W+50)+2W=500}}}
{{{2W+100+2W=500}}}
{{{4W+100=500}}}
{{{4W=400}}}
{{{W=100}}}

{{{L=W+50}}}
{{{L=150}}}


Check:
{{{P=2L+2W=2(150)+2(100)=300+200=500}}} Answer checks.