Caleb earns points on his credit card that he can use towards future purchases.

[Josh]

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.

 

[math_celebrity]

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