The balance of a loan is $2,570 in January, and the monthly payment is $125.50. The relationship between the loan balance, y, and the number of monthly payments made since January, x, can be represented by the equation y = 2,570 - 125.50x. In what months does the loan balance, y, meet the condition, $1,600 < y < $2,000? January February March April May June July August September October November December

Question

Mathematics

Jordyn Ewing

27 February, 02:39

The balance of a loan is $2,570 in January, and the monthly payment is $125.50. The relationship between the loan balance, y, and the number of monthly payments made since January, x, can be represented by the equation y = 2,570 - 125.50x. In what months does the loan balance, y, meet the condition, $1,600 < y < $2,000? January February March April May June July August September October November December

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Johanna Mcknight · Answer 1

1600<2570-125.5x<2000 subtract 2570 from all terms ...

-970<-125.5x<-570 divide all terms by - 125.5 (and reverse signs because of division by a negative!)

7.73>x>4.54 and x is months since January, and since months can only be integers ...

x=[5,7]

So January + 5, 6, and 7 respectively are the three months that satisfy the equation ...

June, July, and August.