Think of A as a constant - with D it's 117 and with M it's 88
So the difference between D and M is 29 (117-88)
We also know that M + D = 161
Let's substitute in the problem We will leave M equal to M and rewrite D as M+29 since it is 29 kg heavier. M + M + 29 -161 or 2M +29 = 161 Subtracting 29 from both sides we get 2M=122 Now divide both sides two and get M=61 Since D is M+29 it is 61+29 or 100kg Finally A + M = 88 A + 61 - 88 Subtract 61 from both sides and get A=17 So there you have it: A=17kg M=61kg D=100kg and it works in all three equation in your problem (try it to check)
There's actually a really slick solution to this problem.
Add all three equations. This results in 2(A+M+D)=366. Dividing by two, we see that A+M+D=183, so 183 is the total of the weights.
$10.75 x 3 1/2 = $37.625 (rounded to the nearest cent: $37.63). $10.75 x 5 = $53.75. $37.625 + $53.75 = $91.375. (rounded to the nearest cent: $91.38) hope this helps