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POTW # Solution

 By: Amelia McDonald
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

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Potw 9 Solution

  • 1. POTW # 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