how much money does each have?

Question

Jane has $10 more than Bill, Bill has $17 more than Tricia, and Tricia has $21 more than Steve. If the total amount of all their money is $111, how much money does each have?

Answer 1

Various solution methods actually illustrate the P in P-E-M-D-A-S, which is what is being taught.  So, using J,B,T, and S as variables:

J = 10 + B

B = 17 + T

T = 21 + S

The total is 111.

111 = J                         +                     B                   +           T       + S

111 = (10+B)                +                  (17+T)             +        (21+S) + S

111 = (10+(17+T))        +               (17+(21+S))       +       (21+S) + S

111 = (10+(17+(21+S)) +              (17+(21+S))        +       (21+S) + S

O.K., now evaluate starting with the innermost Parenthesis:

111 = (10+(38+S)) +              (38+S)       +       21+2S

111 = (48+S) + 38+S + 21+2S

111 = 107  + 4S

4 = 4S

1 = S

So,

 T = 21 + S = 21 + 1 = 22

 B = 17 + T = 17 + 22 = 39

 J =  10 + B = 10 + 39 = 49

 

It is important to get the correct answer, but it is more useful (especially for later) to understand the process that is being used to solve the problem.  Compare solution procedures to see how they compare to P-E-M-D-A-S.

Answer 2

The key is to work backwards using one variable.

Steve has x dollars

Tricia has x+21 dollars

Bill has x+21+17 dollars

Jane has x+21+17+10 dollars

add them together

x+x+21+x+21+17+x+21+17+10=111

4x+107=111

4x=111-107

4x=4

x=1

Steve Has $1

Tricia has $22

Bill has $39

Jane has $49

Answer 3

This was actually pretty fun! Like a puzzle!

 

J = B + 10

B = T + 17

T = S + 21

J+B+T+S = 111

 

 

J = T+17+10

J = T+27

 

B = S+21+17

B = S+38

 

Substitute this new information into equation 4:

 

T+27+S+38+T+S = 111

                 2T+2S = 111-65

                2(T+S) = 46

                     T+S = 23

 

T+S = 23

T-S = 21 (equation 3)

--------------------------

2T   =  44

 T    = 22

 

T+S = 23

22+S = 23

      S = 1

 

Now you can substitute into equation 1 for J and 2 for B:

 

B = T + 17

B = 22 + 17

B = 39

 

J = B + 10

J = 39 + 10

J = 49

 

Now we can check:

 

J + B + T + S = 111 

49+39+22+1 = 111  ??

              111 = 111  So we are correct!