Question

Jen and David owe $22,000 in loans for their two cars. The amount of the loan for Jen’s car is $2,000 less than twice the amount of the loan for David’s car. Call the amount that Jen owes j and the amount that David owes d.

Answer 1

David: $8,000

Jen: $14,000

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

`j + d = 22,000`

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

`j = 2d -2,000`

Solve the system of two equations:

`\left\{\begin{array}{l}j+d=22,000\\j=2d-2,000\end{array}\right.`

Substitute the second equation into the first:

`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`