MULTIPLE CHOICE:

Jen and David owe $21,000 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. How much is each car loan? (Let j represent the amount of Jen's loan and let d represent the amount of David's loan.)

A. d + j = 21,000
2d − 2,000 = j

B. j + d = 21,000
2j − 2,000 = d

C. j + d = 21,000
2j + 23,000 = d

D. j + d = 2,000
2j − 21,000 = d

E. d + j = 2,000
2d − 21,000 = j

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sqdancefan sqdancefan · Answer 1 · 2021-10-12T23:18:12+02:00

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Answer:

A. d + j = 21,000; 2d − 2,000 = j

d = $7,666.67; j = $13,333.33

Step-by-step explanation:

The relationships given in the problem statement are ...

d + j = 21,000 . . . . . the total of the two loans is $21,000

2d -2000 = j . . . . . . Jen's is $2000 less than twice David's

__

These equations can be solved by substituting for j:

d +(2d -2000) = 21000

3d = 23000 . . . . . . . . . . . add 2000, collect terms

d = 23000/3 = 7666.67 . . . divide by the coefficient of d

j = 21000 -d = 21000 -7666.67 = 13333.33

Jen's loan is $13,333.33; David's loan is $7,666.67.