1) The problem gives equations relating variables a, b, c, and d where a+b+c+d=45. 2) Solving the equations for each variable in terms of a yields: a=8, b=12, c=5, d=20. 3) Plugging these values into the original expression a+b+c-d gives the solution of 5.

1. POTW #9 Solution
By: Amelia McDonald

2. Given a+b+c+d=45 and a+2=b-2=2c=d/2 compute
a+b+c-d.
1. Solve each pair for b, c, and 2. Plug in for each variable in 4. Plug in variable
d so that a is the variable. original equation and solve. values into a+b+c-d.
a+2=b-2 a+b+c+d=45 a+b+c-d=
+2 +2 a+(a+4)+((1/2)a+1)+(2a+4)=45 8+12+5-20=
a+4=b (9/2)a+9=45 20+5-20=
-9 -9 25-20=5
b-2=2c (9/2)a=36
(a+4)-2=2c (2/9)(9/2)a=36(2/9) Final Answer=5
((a+4)-2)/2=(2c)/2 a=8
(1/2)a+1=c
3. Find each individual variable.
2c=d/2
2((1/2)a+1)=d/2 a+2=b-2=2c=d/2
1a+2=d/2 8+2=12-2=(2)(5)=20/2
(2)(1a+2)=(d/2)(2) a=8, b=12, c=5, d=20
2a+4=d