Finding factors in known ratio - php

Question

I'm making a calculator for pipe fittings. The idea is that the user inputs the angle of the turn, then the calculator will tell you how many of what fittings to use. I have access to 8°, 11.25°, 22.5°, 45°, and 90° fittings. But, I can simplify it into 8° and 11.25° fittings, since 22.5°, 45°, and 90° are multiples of 11.25. I can take the # of 11.25 degree fittings, then use the following code to break it into larger fittings.
$num90 = floor($angle11 / 90);
$runningtotal = $angle11 - $num90 * 90;
$num45 = floor($runningtotal / 45);
$runningtotal = $runningtotal - $num45 * 45;
$num22 = floor($runningtotal / 22.5);
$runningtotal = $runningtotal - $num22 * 22.5;
$num11 = floor($runningtotal / 11.25);
$runningtotal = $runningtotal - $num11 * 11.25;
echo "You will need:";
echo "<br>";
echo "$num90 -- 90° fittings";
echo "<br>";
echo "$num45 -- 45° fittings";
echo "<br>";
echo "$num22 -- 22.5° fittings";
echo "<br>";
echo "$num11 -- 11.25° fittings";
Basically, I need to solve the equation:
"8x + 11.25y = angle"
Where "angle" is a known value, and X and Y are integers.
I've made a list of all the possible angles using these fittings, so the program will use the closest possible angle to their request (e.g. if they need a 150° turn, they'll be shown the fittings needed for a 150.5° connection, which is possible). That means that X and Y will be whole numbers. I already have the code to select the closest angle, I'm not worried about it.
I've looked into solutions for the Change Making Problem, which deals with something extremely similar. Most of the equations and algorithms they found go way over my head in terms of complexity. I'm a recent high school graduate, so my math level isn't as good as others.
How would I go about solving this equation? Is this maybe too complicated for me, a beginner? Am I overlooking some super simple solution?
Or, should I just use the wolframalpha API to offload the math onto their side?
Any help would be very appreciated!

Answer 1

Try this:
print_r(get_best_fit(150));
function get_best_fit($angle){
$a = 8;
$b = 11.25;
$best_diff = $angle;
$best_fit = [0,0];
for($x = 0; $x <= $angle/$a; $x++){
$y = round(($angle-$a*$x)/$b);
$diff = $angle-($x*$a+$y*$b);
if(abs($diff) < $best_diff){
$best_diff = abs($diff);
$best_fit = [$x,$y];
}
}
return $best_fit;
}
Output
Array ( [0] => 16 [1] => 2 )
So you would need 16 x 8 + 2 x 11.25.