Your friend has loaned you $2500. Each week, you pay back $75 to this friend.

Question

Your friend has loaned you $2500. Each week, you pay back $75 to this friend.

a). Complete the following table, where m = number of months and d = debt owed.

m d

0

1

2

3

b). Write a linear equation to model the debt you have.

c). Write a sentence to interpret the slope of the linear equation.

d). Graph the linear equation, either using points or using the slope and y-intercept.

e). When will the debt be repaid?

Answer 1

debt = 2500 - 75 per week

d = 2500-75w

For example, after 10 weeks...

d = 2500-75(10) = 2500-750 = 1750 remaining debt

After 20 weeks...

d = 2500-75(20) = 2500-1500 = 1000 remaining debt

Graph is a downward slope (decreases as weeks increase) from left to right (At week 0 = 2500).

The debt will be repaid after 34 weeks, with the final payment of $25.

Answer 2

d = 2500 - 75w

in week 0 you owe $2,500

in week 1 you owe $2,500 - 75 = $2,4,25

in 2 weeks you owe 2425 - 150 -= $2275

in 3 weeks you owe 2500 - 3(75) = 2275-225 = $2,050

in W weeks the debt will = 2500-75W

Debt = D =2500 - 75W

2500 -75W =0 when debr is paid off

75W =2500

W= 2500/75 = 33 1/3 weeks.

33rd week won't be enough. 34th week will pay if off and more.

It's a downward sloping line, graphically, with slope =-75, fairly steep. the slope means the debt is reduced by $75 each week.