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

Publish date: 2024-06-14
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

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