We know that there are at least 3 short sleeved shirts and there are at least 7 long sleeved shirts. And we know it's in that ratio. So the best way to start this is to divide 460 by 7+3 to get the single unit amount of both shirts.
46 is the single unit amount. So 46 * 3 will get us our short sleeved shirts:
46 * 3 = 138
To check our answer, we'll take 460-138 and divide that by 7 to see if we get 46:
![60x^3+145x^2+70x=5x(12x^2+29x+14)=5x(12x^2+21x+8x+14)\\\\=5x[3x(4x+7)+2(4x+7)]=5x(4x+7)(3x+2)](https://tex.z-dn.net/?f=60x%5E3%2B145x%5E2%2B70x%3D5x%2812x%5E2%2B29x%2B14%29%3D5x%2812x%5E2%2B21x%2B8x%2B14%29%5C%5C%5C%5C%3D5x%5B3x%284x%2B7%29%2B2%284x%2B7%29%5D%3D5x%284x%2B7%29%283x%2B2%29)
