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Question 1123449: 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?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! your equation is y = 2570 - 125.5 * x
you want to know when 1600 < y < 2000
since y = 2570 - 125.5 * x, then you can replace y with 2570 - 125.5 * x and you then want to know when 1600 < 2570 - 125.5 * x < 2000
subtract 2570 from all sides of this inequality to get:
1600 - 2570 < -125.5 * x < 2570 - 2000
multiply all sides of this inequality by -1 to get:
-(1600 - 2570 > 125.5 * x > -(2570 - 2000)
simplify to get 970 > 125.5 * x > 570
divide all sides of this inequality by 125.5 to get 970 / 125.5 > x > 570 / 125.5
simplify to get 7.729083665 > x > 4.541832669
your answer will be somewhere between 4 and 8.
when x = 4, y = 2570 - 125.5 * x = 2068
when x = 5, y = 2570 - 125.5 * x = 1942.5 which is < 2000
when x = 8, y = 2570 - 125.5 * x = 1566
when x = 7, y = 2570 - 125.5 * x = 1691.5 which is > 1600
your answer is that 1600 < y < 2000 when x = 5 to 7.
you could have analyzed this from the answer of 7.729083665 > x > 4.541832669
if x > 4.541832669, then x > 4 which means x >= 5.
if x < 7.729083665, then x < 8 which means x <= 7.
x >= 5 and x <= 7 gets you x = 5 or 6 or 7, as long as x has to be an integer.
if you're in doubt, then doing it the way i did it above by checking x = 7,8,4,5 is a good way to be sure you got it right.
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