Question 1012290
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Jen, Kathy, and Lou work Together. The ratio of Jen's salary to Kathy's salary is 4:3. Lou makes $4,000 more than Kathy does. 
If the total of their salaries is $134,000, how much does each person make?
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Mathematical model is this system of equations

{{{J/K}}} = {{{4/3}}},                  (1)
K + 4000 = L,             (2)
J + K + L = 134000,       (3)

or

J = {{{(4/3)*K}}},               (4)
K = L - 4000,             (5)
J + K + L = 134000.       (6)

Express J via L by substituting (5) into (4): 

J = {{{(4/3)*(L-4000)}}}.       (7)

Now substitute (7) and (5) into (6). You will get a single equation for L:

{{{(4/3)*(L-4000) + (L-4000) + L}}} = 134000.

Multiply both sides by 3:

4*(L-4000) + 3*(L-4000) + 3L = 134000*3 = 402000.

Simplify and solve for L:

10L - 28000 = 402000  ----->   10L = 430000  -----> L = {{{430000/10}}} = 43000.

Now you can easily find the rest of unknowns: 

K = L - 4000 = 43000 - 4000 = 39000,

J = {{{(4/3)*K}}} = {{{(4/3)*39000}}} = 4*13000 = 52000.

<U>Answer</U>. J = 52000, K = 39000, L = 43000.
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