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.
Ms. Sue can you please help me eliminate some of the options.
25x = 500.
X = 20 Weeks to pay off the debt.
Even though my choice is "a", I don't understand Greg's Eq. Are you sure it is correct? The amount owed increases as x increases.
Could it be Y = 600-20x? If so, then Greg would pay off his debt in 30 weeks: Y = 600-20x = 0, X = 30 weeks.
To compare Greg's function and Lin's function, we can directly compare the equations and their variables.
For Greg's bike:
- Equation: y = 20x + 600
- The coefficient of x, which represents the amount paid each week, is 20.
- The initial amount owed is $600.
For Lin's bike:
- Equation: y = 25x
- The coefficient of x, which represents the amount paid each week, is 25.
- The initial amount owed is $500.
Now, let's go through each statement to determine which one is correct:
a) Lin's bike cost less than Greg's bike?
To compare the cost of the bikes, we compare the initial amounts owed. Lin's bike costs $500, while Greg's bike costs $600. Therefore, Lin's bike cost less than Greg's bike.
b) Lin's bike will be paid off after Greg's bike?
To determine when the bikes will be paid off, we check the x-intercept of each function. Since the x-intercept is the point where y equals zero, we set each equation equal to zero and solve for x.
For Greg's bike: 0 = 20x + 600
Solving, we find x = -30.
For Lin's bike: 0 = 25x
Solving, we find x = 0.
Since Lin's bike has a zero x-intercept, it means that she will pay off the bike before Greg, who has a negative x-intercept. Therefore, Lin's bike will be paid off before Greg's bike.
c) Lin is paying less money each week for the bike?
To compare the amount paid each week, we compare the coefficients of x. Lin pays $25 each week, while Greg pays $20 each week. Therefore, Lin is paying more money each week for the bike, not less.
d) Lin will have more left to pay than Greg after 10 weeks?
To determine the amount left to pay after 10 weeks, we substitute x = 10 into each function and find the corresponding y-values.
For Greg's bike: y = 20(10) + 600 = 800
For Lin's bike: y = 25(10) = 250
Therefore, after 10 weeks, Lin will have less left to pay ($250) compared to Greg ($800). Thus, the statement is incorrect.
Based on the analysis, the correct statement is: a) Lin's bike cost less than Greg's bike.