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?
Answers
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.
Answer:
June, July, and August.
Step-by-step explanation:
We can solve it the hard way but I will show you how to do the easy way :]
y = 2,570 - 125.50x
= 2,570 [balance of the loan in January]
= 2,570 - 125.50x
= 2, 444 [balance of the loan in February]
= 2, 444 - 125.50x
= 2,319 [balance of the loan in March]
= 2,319 - 125.50x
= 2,193.50 [balance of the loan in April]
= 2,193.50 - 125.50x
= 2,068 [balance of the loan in May]
= 2,068 - 125.50x
= 1,942.50 [balance of the loan in June]
= 1,942.50 - 125.50x
= 1,812 [balance of the loan in July]
= 1,812 - 125.50x
= 1,691.50 [balance of the loan in August]
= 1,691.50 - 125.50x
= 1566 [balance of the loan in September]
-We can stop in September because the given condition states,
"$1,600 < y < $2,000?"
The loans every month expresses "y", and we can see that June, July, and August fit our solution if we substitute their values to "y".
So if we substitute the values from the months June, July, and August from y, it meets the condition [y is greater than $1,600, but $2,000 is greater than y.]
I hope I helped, Stay safe and God bless :]