Points are earned as:
- 4 points per $ spent on flights
- 2 points per $ spent at hotels
- 1 point per $ spent on all other purchases
Total money spent on credit card last year = $9,480
Total points earned through credit card last year = 14,660 points
Money spent on flight = 140 + 2 × Money spent on hotels
Let money spent on flights be 'a', money spent on hotels be 'b' and money spent on other things be 'c'
⇒ Total money spent on credit card last year = a + b + c = 9,480 ........ (i)
And, Total points earned through credit card last year = 4×a + 2×b + c = 14,660 ........... (ii)
Also, a = 140 + 2×b ............. (iii)
Substitute (iii) in (i) and (ii)
(i): 140 + 2b + b + c = 9,480
⇒ 140 + 3b + c = 9,480
⇒ 3b + c = 9,340 .......... (iv)
(ii): 4×(140 + 2b) + 2b + c = 14,660
⇒ 560 + 8b + 2b + c = 14,660
⇒ 10b + c = 14,100 ....... (v)
Subtracting (iv) from (v)
7b = 4,760
⇒ b = 680
Substituting value of b in (iii)
a = 140 + 2×680
⇒ a = 1,500
Substituting value of 'a' and 'b' in (i)
1,500 + 680 + c = 9,480
⇒ c = 7,300
Hence, Caleb spent $680 on flights, $1,500 on hotels and $7,300 on other purchases
