a. The amount of money Rustam owes his parents, y, after a months can be represented by the equation: y = 1000 - 100a where a represents the number of months.
b. The amount of money Val owes his parents, y, after a months can be represented by the equation: y = 800 - 50a where a represents the number of months.
c. To find the intersection of the graphs of the equations from parts a and b, we need to solve the system of equations: 1000-100a = 800 - 50a Rearranging the equation: 200 = 50a Dividing both sides by 50: 4 = a So the ordered pair (4, 600) represents the intersection of the graphs. In the context of this problem, it means that after 4 months, both Rustam and Val owe their parents a total of $600.
d. To determine who will take longer to pay their parents back, we compare the values of a. Rustam pays $100 each month, so it would take him 10 months to fully pay back his parents (1000/100 = 10). Val pays $50 each month, so it would take him 16 months to fully pay back his parents (800/5016). Therefore, Val will take longer to pay his parents back.
