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Robert borrowed $750 from his parents. He promised to repay the loan by giving his parents at least $67 from his paycheck each week Assuming Robert sticks to his promise, which of the following is NOT a possible scenario for the amount of debt Robert has remaining?

A.) after 5 weeks, Robert is $150 in debt

B.) after 6 weeks, Robert is $200 in debt

C.) after 7 weeks, Robert is $250 in debt

D.) after 8 weeks, Robert is $300 in debt

Respuesta :

carlosego

To answer this question we can propose the following equation:


[tex]d=750 -x(67)[/tex]


Where:


x is the number of weeks elapsed.


d is the debt depending on the weeks.



Robert promised to pay at least $ 67 each week.


Therefore, after 5 weeks the debt of rober should be:


[tex]d\leq750-5*67[/tex]

[tex]d\leq415[/tex]


Then scenario A) is possible because [tex]150<415[/tex].



After 6 weeks:


[tex]d\leq750-6*67[/tex]


[tex]d\leq348[/tex]

Then scenario B) is possible because [tex]200<348[/tex].



After 7 weeks


[tex]d\leq750-7*67[/tex]


[tex]d\leq281[/tex]

Then scenario C) is possible because [tex]250 <281[/tex].



After 8 weeks

[tex]d\leq750-8*67[/tex]

[tex]d\leq214[/tex]

So scenario D) is NOT possible because [tex]300>214[/tex]



Finally the correct answer is option D.

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