y:x = 3:4 can be reversed to say x:y = 4:3. y:z = 2:3. If we make the y terms into the same number, in this case 6, we can create what's called an extended ratio. So
x:y = 8:6 and y:z = 6:9 so the ratio of x:y:z = 8:6:9 . Using the ratio factor method, that is if we multiply each number by the same factor, the numbers change but the ratio stays the same, we can write 8r +6r+9r = 1800. So 23r =1800 and r=1800/3. Not a very nice number!!!! But we'll go with it. Plug it back into the ratio then round to nearest hundredth since we're dealing with money.
x = 8*1800/23 = $626.09
y = 6*1800/23 = $469.57
z = 9*1800/23 = $704.35
let's check these since they're such bizarre answers. Remember we rounded these off so it won't come out exact but should be close.
626.09 + 469.57 + 704.35 = 1800.01 pretty close I'd say.
y:x = 3:4 =0.75 our y/x is 469.57/ 626.09 = 0.750003993 pretty close!!!!
y:z = 2:3 = 0.6666666666 OUR y:z is 469.57 / 704.35 = 0.666671399 pretty darn close
So you got some strange answers, but they work!!!!