Answer:
David: $8,000
Jen: $14,000
Step-by-step explanation:
The amount that Jen owes = j
The amount that David owes = d
Jen and David owe $22,000 in loans for their two cars, then
[tex]j + d = 22,000[/tex]
The amount of the loan for Jen’s car is $2,000 less than twice the amount of the loan for David’s car, then
- twice the amount of the loan for David’s car = 2d
- $2,000 less than twice the amount of the loan for David’s car = 2d - 2,000
then
[tex]j = 2d -2,000[/tex]
Solve the system of two equations:
[tex]\left\{\begin{array}{l}j+d=22,000\\j=2d-2,000\end{array}\right.[/tex]
Substitute the second equation into the first:
[tex]2d-2,000+d=22,000\\ \\3d=24,000\\ \\d=8,000\\ \\j=2\cdot 8,000-2,000=16,000-2,000=14,000[/tex]
