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.
To compare Greg's function (y = 20x + 600) with Lin's function, we need to determine Lin's function.
Lin is buying a bike for $500 and will pay $25 each week.
Let's assume x represents the number of weeks and y represents the amount Lin has left to pay.
For Lin's function, we can use the equation y = 25x + b, where b is the initial amount Lin owes.
Since Lin owes $500 initially, the equation becomes y = 25x + 500.
Now let's compare Greg's function with Lin's function using the given options:
a) Lin's bike cost less than Greg's bike?
Lin's bike costs $500, while Greg's bike is not specified. Therefore, we cannot determine if Lin's bike costs less.
b) Lin's bike will be paid off after Greg's bike?
To determine this, we need to find the number of weeks it would take to pay off each bike.
For Greg's bike, y = 0 (fully paid), so we can solve 0 = 20x + 600 for x.
20x = -600
x = -600/20
x = -30
Since the number of weeks cannot be negative, it will take Greg more than 30 weeks to pay off the bike.
For Lin's bike, we can solve 0 = 25x + 500 for x.
25x = -500
x = -500/25
x = -20
Similarly, since the number of weeks cannot be negative, it will take Lin more than 20 weeks to pay off the bike.
Therefore, we cannot determine if Lin's bike will be paid off after Greg's bike.
c) Lin is paying less money each week for the bike?
Greg is paying $20 each week, while Lin is paying $25 each week. Therefore, Lin is paying more money each week for the bike.
d) Lin will have more left to pay than Greg after 10 weeks?
To determine this, we can substitute x = 10 into both functions and compare the values of y.
For Greg's function, y = 20(10) + 600 = 800.
For Lin's function, y = 25(10) + 500 = 750.
Therefore, Greg will have more left to pay than Lin after 10 weeks.
Based on the explanations above, option d) "Lin will have more left to pay than Greg after 10 weeks" is the correct statement.
'the equation y=20x+600 models the amount he has left to pay, where x is the number of weeks'
x will always have a positive value, and if y is the amount he has LEFT TO PAY, then as time goes on, he will owe an increasing amount, which isn't how it should be.
Perhaps the equation is y = -20x + 600, which would mean he pays $20 every week?