Caleb earns points on his credit card that he can use towards future purchases. He earns four points per dollar spent on flights, two points per dollar spent on hotels, and one point per dollar spent on all other purchases. Last year, he charged a total of $9,480 and earned 14,660 points. The amount of money spent on flights was $140 money than twice the amount of money spent on hotels. Find the amount of money spent on each type of purchase.
Let f = dollars spent on flights, h dollars spent on hotels, and p dollars spent on all other purchases. Set up our equations: (1) 4f + 2h + p = 14660 (2) f + h + p = 9480 (3) f = 2h + 140 First, substitute (3) into (2) (2h + 140) + h + p = 9480 3h + p + 140 = 9480 3h + p = 9340 Subtract 3h to isolate p to form equation (4) (4) p = 9340 - 3h Take (3) and (4), and substitute into (1) 4(2h + 140) + 2h + (9340 - h) = 14660 Multiply through 8h + 560 + 2h + 9340 - 3h = 14660 Combine h terms and constants (8 + 2 - 3)h + (560 + 9340) = 14660 7h + 9900 = 14660 Subtract 9900 from both sides: 7h = 4760 Divide each side by 7 h = 680 Substitute h = 680 into equation (3) f = 2(680) + 140 f = 1360 + 140 f = 1,500 Substitute h = 680 and f = 1500 into equation (2) 1500 + 680 + p = 9480 p + 2180 = 9480 Subtract 2180 from each side: p = 7,300
