Greg is buying a bike on a payment plan. the equation y=20x+600 models the amount he has left to pay, where x is the number of weeks and y is the amount of money owed in dollars. Lin is also buying a bike on a payment plan. The bike costs $500. She will pay $25 each week. Which statement correctly compares Greg's function and Lin's function.
a) Lin's bike cost less than Greg's bike?
b) Lin's bike will be paid off after Greg's bike?
c) Lin is paying less money each week for the bike?
d) Lin will have more left to pay than Greg after 10 weeks?
Not sure on this one.
You didn't reply to my clarification when I replied to this question earlier.
I'll assume that the first equation is y= -20x + 600
This means that Greg pays $20 every week, and the total amount he has to pay is $600.
On the other hand, Lin owes $500 total, and pays $25 every week.
Hence, the correct answer is (a)
the equation is y=20x+600
To compare Greg's function and Lin's function, let's first look at their respective equations.
Greg's equation: y = 20x + 600
Lin's equation: y = -25x + 500
a) Lin's bike cost less than Greg's bike?
To compare the cost of their bikes, we can compare the y-intercept (the value when x = 0). In Lin's equation, the y-intercept is 500, which means her bike costs $500. In Greg's equation, the y-intercept is 600, which means his bike costs $600. Therefore, Lin's bike costs less than Greg's bike.
The correct statement is (a) Lin's bike cost less than Greg's bike.
b) Lin's bike will be paid off after Greg's bike?
To determine which bike will be paid off first, we need to compare the x-intercept (the value when y = 0). In Greg's equation, the x-intercept is -600/20 = -30. In Lin's equation, the x-intercept is -500/-25 = 20. This means that Lin's bike will be paid off after 20 weeks, while Greg's bike will be paid off after 30 weeks.
The statement that Lin's bike will be paid off after Greg's bike is incorrect.
c) Lin is paying less money each week for the bike?
We can compare the coefficients of x in each equation. In Greg's equation, the coefficient of x is 20, meaning he pays $20 per week. In Lin's equation, the coefficient of x is -25, meaning she pays $25 per week. Therefore, Lin is paying more money each week for the bike.
The statement that Lin is paying less money each week for the bike is incorrect.
d) Lin will have more left to pay than Greg after 10 weeks?
To find out the amount left to pay after a certain number of weeks, we substitute the value of x into the equations. After 10 weeks:
Greg: y = 20(10) + 600 = 800
Lin: y = -25(10) + 500 = 250
After 10 weeks, Greg will have $800 left to pay, while Lin will have $250 left to pay. Therefore, Lin will have less left to pay than Greg after 10 weeks.
The statement that Lin will have more left to pay than Greg after 10 weeks is incorrect.
In conclusion, the correct statement is (a) Lin's bike cost less than Greg's bike.